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'''Paul Allen Catlin''' ({{dob|1948|6|25}} – {{Date of death|1995|4|20}}) was a mathematician, professor of mathematics and Doctor of Mathematics, known for his valuable contributions to [[graph theory]] and [[number theory]]. He wrote one of the most cited papers in the series of chromatic numbers and Brooks' theorem, entitled '' Hajós graph coloring conjecture: variations and counterexamples''.<ref name=catlin> {{cite journal |last1=Hobbs |first1=Arthur M. |last2= Lai |first2= Hong-Jian |last3= Robertson |first3= Neil |authorlink3=Neil Robertson (mathematician) |title= Paul Catlin 1948–1995 |chapter= Preface |journal= Discrete Mathematics |year=2001 |volume= 230 |issue=1-3 |pages= 3–12 |url= http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/ListPublicationsCatlin.htm }}</ref> <ref> {{cite web |url= http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/c/Catlin:Paul_A=.html |title= List of publications of Paul A. Catlin |work= [[Dagstuhl|Leibniz Center for Informatics]] }}</ref> <ref name=list> {{cite web |url=http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/ListPublicationsCatlin.htm |title=Publications of Paul A. Catlin |work=West Virginia Universiy }}</ref>
'''Paul Allen Catlin''' ({{birth date|1948|6|25}} – {{Date of death|1995|4|20}}) was a mathematician, professor of mathematics and Doctor of Mathematics, known for his valuable contributions to [[graph theory]] and [[number theory]]. He wrote one of the most cited papers in the series of chromatic numbers and Brooks' theorem, entitled '' Hajós graph coloring conjecture: variations and counterexamples''.<ref name=catlin>{{cite journal |last1=Hobbs |first1=Arthur M. |last2= Lai |first2= Hong-Jian |last3= Robertson |first3= Neil |authorlink3=Neil Robertson (mathematician) |title= Paul Catlin 1948–1995 |chapter= Preface |journal= Discrete Mathematics |year=2001 |volume= 230 |issue=1-3 |pages= 3–12 |url= http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/ListPublicationsCatlin.htm }}</ref><ref>{{cite web |url= http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/c/Catlin:Paul_A=.html |title= List of publications of Paul A. Catlin |work= [[Dagstuhl|Leibniz Center for Informatics]] }}</ref><ref name=list>{{cite web |url=http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/ListPublicationsCatlin.htm |title=Publications of Paul A. Catlin |work=West Virginia Universiy }}</ref>


==Career==
==Career==


He held a Doctorate in Mathematics degree from [[Ohio State University]], authored over fifty academic papers in [[number theory]] and [[graph theory]]. Many of his contributions and collaborations have been published in [[Fibonacci Quarterly|The Fibonacci Quaterly]], in [[Journal of Number Theory|The Journal of Number Theory]], in the journal of [[Discrete Mathematics (journal)|Discrete Mathematics]], and many other academic publications. <ref name=list/> He has co-authored scholarly papers with Arthur M. Hobbs <ref name=coauthors> {{cite web |url= http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/c/Catlin:Paul_A=.html#coauthors |title= Coauthor index |work = Leibniz Center for Informatics }} </ref>, [[Béla Bollobás]] and [[Paul Erdős]] <ref name=hadwiger> {{cite journal
He held a Doctorate in Mathematics degree from [[Ohio State University]], authored over fifty academic papers in [[number theory]] and [[graph theory]]. Many of his contributions and collaborations have been published in [[Fibonacci Quarterly|The Fibonacci Quaterly]], in [[Journal of Number Theory|The Journal of Number Theory]], in the journal of [[Discrete Mathematics (journal)|Discrete Mathematics]], and many other academic publications.<ref name=list/> He has co-authored scholarly papers with Arthur M. Hobbs,<ref name=coauthors>{{cite web |url= http://www.informatik.uni-trier.de/~ley/db/indices/a-tree/c/Catlin:Paul_A=.html#coauthors |title= Coauthor index |work = Leibniz Center for Informatics }}</ref> [[Béla Bollobás]] and [[Paul Erdős]],<ref name=hadwiger>{{cite journal
|author= Paul A. Catlin
|author= Paul A. Catlin
|author2 = Béla Bollobás
|author2 = Béla Bollobás
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|year= 1980
|year= 1980
|url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin18.pdf
|url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin18.pdf
}} </ref>, [[Hong-Jian Lai]], Zheng-Yiao Han, and Yehong Shao <ref name=coauthors/>, among others. He also published papers with [[Neil Robertson (mathematician)|G. Neil Robertson]], with whom he also completed his dissertation thesis in 1976. <ref name=catlin/> <ref>{{cite thesis |type=Ph.D. |first=Paul A |last=Catlin |title=Embedding subgraphs and coloring graphs under extremal degree conditions |publisher=Ohio State University |year=1976 |url=http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Dissertation_1.pdf }}</ref> <ref name=catlin/>
}}</ref> [[Hong-Jian Lai]], Zheng-Yiao Han, and Yehong Shao,<ref name=coauthors/> among others. He also published papers with [[Neil Robertson (mathematician)|G. Neil Robertson]], with whom he also completed his dissertation thesis in 1976.<ref name=catlin/><ref name=catlin/><ref>{{cite thesis |type=Ph.D. |first=Paul A |last=Catlin |title=Embedding subgraphs and coloring graphs under extremal degree conditions |publisher=Ohio State University |year=1976 |url=http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Dissertation_1.pdf }}</ref>


Originally from [[Bridgeport]], [[Connecticut]], he majored in Mathematics with a B.A. degree from [[Carnegie Mellon University]] in 1970. <ref name=catlin/>
Originally from [[Bridgeport]], [[Connecticut]], he majored in Mathematics with a B.A. degree from [[Carnegie Mellon University]] in 1970.<ref name=catlin/>


From 1972 to 1973, he was a research and teaching assistant at [[Ohio State University]], where he earned the Master of Science degree in Mathematics. <ref name=catlin/>
From 1972 to 1973, he was a research and teaching assistant at [[Ohio State University]], where he earned the Master of Science degree in Mathematics.<ref name=catlin/>


In 1976, he went to work at [[Wayne State University]], where he concentrated the research on [[Graph_coloring#Definition_and_terminology|chromatic numbers]] and [[Brooks' theorem]]. As a result, '''Paul A. Catlin''' published one of the most cited papers in that series: ''Hajós graph coloring conjecture: variations and counterexamples.'' <ref name=catlin/> <ref> {{cite journal
In 1976, he went to work at [[Wayne State University]], where he concentrated the research on [[Graph_coloring#Definition_and_terminology|chromatic numbers]] and [[Brooks' theorem]]. As a result, '''Paul A. Catlin''' published one of the most cited papers in that series: ''Hajós graph coloring conjecture: variations and counterexamples.'',<ref name=catlin/><ref>{{cite journal
|author = Paul A. Catlin
|author = Paul A. Catlin
|title = Hajós' graph-coloring conjecture: Variations and counterexamples
|title = Hajós' graph-coloring conjecture: Variations and counterexamples
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|doi = 10.1016/0095-8956(79)90062-5
|doi = 10.1016/0095-8956(79)90062-5
|url= http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin14.pdf
|url= http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin14.pdf
}} </ref>, which showed that the conjecture raised by [[Hugo Hadwiger]] is further strenghtened not only by <math> k \le 4 </math> but also by <math> k \ge 7 </math> <ref> [[Hadwiger conjecture (graph theory)#Generalizations|Hadwiger's conjecture generalizations]] </ref>, which led to the joint paper written with [[Paul Erdős]] and [[Béla Bollobás]] entitled ''Hadwiger's conjecture is true for almost every graph''. <ref name=hadwiger/>
}}</ref> which showed that the conjecture raised by [[Hugo Hadwiger]] is further strenghtened not only by <math> k \le 4 </math> but also by <math> k \ge 7 </math>,<ref>[[Hadwiger conjecture (graph theory)#Generalizations|Hadwiger's conjecture generalizations]]</ref> which led to the joint paper written with [[Paul Erdős]] and [[Béla Bollobás]] entitled ''Hadwiger's conjecture is true for almost every graph''.<ref name=hadwiger/>


==Published academic papers==
==Published academic papers==
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|volume = 309
|volume = 309
|year = 2009
|year = 2009
|pages = 1033--1040
|pages = 1033–1040
|issue = 5
|issue = 5
|doi = 10.1016/j.disc.2007.11.056
|doi = 10.1016/j.disc.2007.11.056
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|volume = 230
|volume = 230
|year = 2001
|year = 2001
|pages = 71--97
|pages = 71–97
|issue = 1-3
|issue = 1-3
|doi = 10.1016/S0012-365X(00)00071-6
|doi = 10.1016/S0012-365X(00)00071-6
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|year = 1977
|year = 1977
|volume = 19
|volume = 19
|pages = 136-45
|pages = 136–45
|url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin08.pdf
|url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin08.pdf
}}
}}
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|volume = 160
|volume = 160
|year = 1996
|year = 1996
|pages = 81--91
|pages = 81–91
|issue = 1-3
|issue = 1-3
|doi = 10.1016/S0012-365X(95)00149-Q
|doi = 10.1016/S0012-365X(95)00149-Q
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|volume = 160
|volume = 160
|year = 1996
|year = 1996
|pages = 67--80
|pages = 67–80
|issue = 1-3
|issue = 1-3
|doi = 10.1016/0012-365X(95)00150-U
|doi = 10.1016/0012-365X(95)00150-U
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|volume= 77
|volume= 77
|issue= 1
|issue= 1
|pages= 60-61
|pages= 60–61
|url= http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin01.pdf
|url= http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin01.pdf
}}
}}
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|volume = 12
|volume = 12
|issue= 4
|issue= 4
|pages= 349-50
|pages= 349–50
|url= http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin03.pdf
|url= http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin03.pdf
}}
}}
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|year = 1974
|year = 1974
|volume= 12
|volume= 12
|pages = 365-68
|pages = 365–68
|url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin04.pdf
|url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin04.pdf
}}
}}
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|year = 1990
|year = 1990
|volume = 74
|volume = 74
|pages = 233-38
|pages = 233–38
|url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin35.pdf
|url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin35.pdf
}}
}}
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|volume = 66
|volume = 66
|year = 1996
|year = 1996
|pages = 123--139
|pages = 123–139
|issue = 1
|issue = 1
|doi = 10.1006/jctb.1996.0009
|doi = 10.1006/jctb.1996.0009
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|volume = 26
|volume = 26
|year = 1979
|year = 1979
|pages = 268--274
|pages = 268–274
|issue = 2
|issue = 2
|doi = 10.1016/0095-8956(79)90062-5
|doi = 10.1016/0095-8956(79)90062-5
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|year = 1979
|year = 1979
|issue = 1
|issue = 1
|pages = 42-48
|pages = 42–48
}}
}}
* {{cite journal
* {{cite journal
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|volume = 22
|volume = 22
|year = 1996
|year = 1996
|pages = 151--153
|pages = 151–153
|issue = 2
|issue = 2
|doi = 10.1002/(SICI)1097-0118(199606)22:2<151::AID-JGT5>3.0.COand2-M
|doi = 10.1002/(SICI)1097-0118(199606)22:2<151::AID-JGT5>3.0.COand2-M
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|editor-last = Alavi
|editor-last = Alavi
|editor-first = Yousef
|editor-first = Yousef
|editor-last2 = Schwenk
|editor2-last = Schwenk
|editor-first2 = Allen
|editor2-first = Allen
|editor-last3 = Chartrand
|editor3-last = Chartrand
|editor-first3 = G
|editor3-first = G
|title = Graph Theory, Combinatorics, and Applications
|title = Graph Theory, Combinatorics, and Applications
|chapter = Spanning trails joining two given edges
|chapter = Spanning trails joining two given edges
|year = 1991
|year = 1991
|publisher = Wiley and Sons, Inc.
|publisher = Wiley and Sons, Inc.
|pages = 207-22
|pages = 207–22
|url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin38.pdf
|url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin38.pdf
}}
}}
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|volume = 141
|volume = 141
|year = 1995
|year = 1995
|pages = 37--46
|pages = 37–46
|issue = 1-3
|issue = 1-3
|doi = 10.1016/0012-365X(93)E0205-I
|doi = 10.1016/0012-365X(93)E0205-I
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|volume = 16
|volume = 16
|year = 1992
|year = 1992
|pages = 177--196
|pages = 177–196
|issue = 2
|issue = 2
|doi = 10.1002/jgt.3190160209
|doi = 10.1002/jgt.3190160209
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|volume = 40
|volume = 40
|year = 1992
|year = 1992
|pages = 285--302
|pages = 285–302
|issue = 3
|issue = 3
|doi = 10.1016/0166-218X(92)90002-R
|doi = 10.1016/0166-218X(92)90002-R
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|volume = 21
|volume = 21
|year = 1978
|year = 1978
|pages = 189-93
|pages = 189–93
}}
}}
* {{cite book
* {{cite book
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|title = Graph theory, combinatorics, algorithms, and applications
|title = Graph theory, combinatorics, algorithms, and applications
|year = 1991
|year = 1991
|pages = 83-95
|pages = 83–95
|url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin39.pdf
|url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin39.pdf
}}
}}
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|volume = 14
|volume = 14
|year = 1990
|year = 1990
|pages = 347--364
|pages = 347–364
|issue = 3
|issue = 3
|doi = 10.1002/jgt.3190140308
|doi = 10.1002/jgt.3190140308
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|volume = 13
|volume = 13
|year = 1989
|year = 1989
|pages = 465--483
|pages = 465–483
|issue = 4
|issue = 4
|doi = 10.1002/jgt.3190130408
|doi = 10.1002/jgt.3190130408
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|volume = 76
|volume = 76
|year = 1989
|year = 1989
|pages = 95--116
|pages = 95–116
|issue = 2
|issue = 2
|doi = 10.1016/0012-365X(89)90303-8
|doi = 10.1016/0012-365X(89)90303-8
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|volume = 12
|volume = 12
|year = 1988
|year = 1988
|pages = 29--44
|pages = 29–44
|issue = 1
|issue = 1
|doi = 10.1002/jgt.319012010
|doi = 10.1002/jgt.319012010
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|volume = 8
|volume = 8
|year = 1988
|year = 1988
|pages = 313--321
|pages = 313–321
|issue = 4
|issue = 4
|doi = 10.1007/BF02189088
|doi = 10.1007/BF02189088
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|volume = 45
|volume = 45
|year = 1988
|year = 1988
|pages = 199--211
|pages = 199–211
|issue = 2
|issue = 2
|doi = 10.1016/0095-8956(88)90069-X
|doi = 10.1016/0095-8956(88)90069-X
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|title= Homomorphisms of 3-chromatic graphs, II
|title= Homomorphisms of 3-chromatic graphs, II
|year= 1985
|year= 1985
|pages= 19-28
|pages= 19–28
|url= http://carbon.ucdenver.edu/~egethner/MikeAlbertson/Papers/AlbertsonCatlin_Homom3ChromaticII_1985.pdf
|url= http://carbon.ucdenver.edu/~egethner/MikeAlbertson/Papers/AlbertsonCatlin_Homom3ChromaticII_1985.pdf
}}
}}
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|volume = 11
|volume = 11
|year = 1987
|year = 1987
|pages = 161--167
|pages = 161–167
|issue = 2
|issue = 2
|doi = 10.1002/jgt.3190110206
|doi = 10.1002/jgt.3190110206
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|volume= 58
|volume= 58
|year= 1987
|year= 1987
|pages= 233-46
|pages= 233–46
|url= http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin23.pdf
|url= http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin23.pdf
}}
}}
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|volume = 25
|volume = 25
|year = 1988
|year = 1988
|pages = 115-24
|pages = 115–24
|url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin24.pdf
|url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin24.pdf
}}
}}
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|volume = 30
|volume = 30
|year = 1981
|year = 1981
|pages = 224--227
|pages = 224–227
|issue = 2
|issue = 2
|doi = 10.1016/0095-8956(81)90066-6
|doi = 10.1016/0095-8956(81)90066-6
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|volume = 27
|volume = 27
|year = 1979
|year = 1979
|pages = 42--48
|pages = 42–48
|issue = 1
|issue = 1
|doi = 10.1016/0095-8956(79)90066-2
|doi = 10.1016/0095-8956(79)90066-2
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|volume = 27
|volume = 27
|year = 1979
|year = 1979
|pages = 149--170
|pages = 149–170
|issue = 2
|issue = 2
|doi = 10.1016/0012-365X(79)90106-7
|doi = 10.1016/0012-365X(79)90106-7
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|volume = 328
|volume = 328
|year = 1979
|year = 1979
|pages = 95--99
|pages = 95–99
|issue = 1 Topics i
|issue = 1 Topics i
|doi = 10.1111/j.1749-6632.1979.tb17770.x
|doi = 10.1111/j.1749-6632.1979.tb17770.x
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|volume = 50
|volume = 50
|year = 1985
|year = 1985
|pages = 179-86
|pages = 179–86
|url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin21.pdf
|url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin21.pdf
}}
}}
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|volume = 22
|volume = 22
|year = 1978
|year = 1978
|pages = 81--83
|pages = 81–83
|issue = 1
|issue = 1
|doi = 10.1016/0012-365X(78)90049-3
|doi = 10.1016/0012-365X(78)90049-3
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|volume = 24
|volume = 24
|year = 1978
|year = 1978
|pages = 1--6
|pages = 1–6
|issue = 1
|issue = 1
|doi = 10.1016/0012-365X(78)90167-X
|doi = 10.1016/0012-365X(78)90167-X
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|volume = 2
|volume = 2
|year = 1978
|year = 1978
|pages = 165--170
|pages = 165–170
|issue = 2
|issue = 2
|doi = 10.1002/jgt.3190020210
|doi = 10.1002/jgt.3190020210
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|volume = 74
|volume = 74
|year = 1990
|year = 1990
|pages = 233-38
|pages = 233–38
}}
}}
* {{cite journal
* {{cite journal
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|volume = 8
|volume = 8
|year = 1976
|year = 1976
|pages = 282--288
|pages = 282–288
|issue = 3
|issue = 3
|doi = 10.1016/0022-314X(76)90006-8
|doi = 10.1016/0022-314X(76)90006-8
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|volume = 8
|volume = 8
|year = 1976
|year = 1976
|pages = 289--297
|pages = 289–297
|issue = 3
|issue = 3
|doi = 10.1016/0022-314X(76)90007-X
|doi = 10.1016/0022-314X(76)90007-X
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|volume = 10
|volume = 10
|year = 1974
|year = 1974
|pages = 225--233
|pages = 225–233
|issue = 2
|issue = 2
|doi = 10.1016/0012-365X(74)90119-8
|doi = 10.1016/0012-365X(74)90119-8
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|volume= 230
|volume= 230
|issue= 1-3
|issue= 1-3
|pages= 71-97
|pages= 71–97
}}
}}


==References==
==References==
{{reflist}}
{{reflist}}


{{Authority control |VIAF= 215369769|LCCN= |GND= |SELIBR= |ORCID= |BNF= |BPN= |RID= |BIBSYS= |ULAN= }}
{{Authority control |VIAF= 215369769|LCCN= |GND= |SELIBR= |ORCID= |BNF= |BPN= |RID= |BIBSYS= |ULAN= }}

<!-- Metadata: see [[Wikipedia:Persondata]] -->
<!-- Metadata: see [[Wikipedia:Persondata]] -->
{{Persondata
{{Persondata
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| PLACE OF DEATH = [[Detroit]] [[Michigan]]
| PLACE OF DEATH = [[Detroit]] [[Michigan]]
}}
}}

{{DEFAULTSORT:Catlin, Paul}}
{{DEFAULTSORT:Catlin, Paul}}
[[Category:1948 births]]
[[Category:1948 births]]

Revision as of 01:18, 16 January 2013

Paul Allen Catlin
Born(1948-06-25)June 25, 1948
DiedApril 20, 1995(1995-04-20) (aged 46)
Alma materOhio State University
Known forGraph theory
Number theory
Scientific career
FieldsMathematics
Thesis Embedding subgraphs and coloring graphs under extremal degree conditions  (1976)
Doctoral advisorG. Neil Robertson

Paul Allen Catlin ((1948-06-25)June 25, 1948 – (1995-04-20)April 20, 1995) was a mathematician, professor of mathematics and Doctor of Mathematics, known for his valuable contributions to graph theory and number theory. He wrote one of the most cited papers in the series of chromatic numbers and Brooks' theorem, entitled Hajós graph coloring conjecture: variations and counterexamples.[1][2][3]

Career

He held a Doctorate in Mathematics degree from Ohio State University, authored over fifty academic papers in number theory and graph theory. Many of his contributions and collaborations have been published in The Fibonacci Quaterly, in The Journal of Number Theory, in the journal of Discrete Mathematics, and many other academic publications.[3] He has co-authored scholarly papers with Arthur M. Hobbs,[4] Béla Bollobás and Paul Erdős,[5] Hong-Jian Lai, Zheng-Yiao Han, and Yehong Shao,[4] among others. He also published papers with G. Neil Robertson, with whom he also completed his dissertation thesis in 1976.[1][1][6]

Originally from Bridgeport, Connecticut, he majored in Mathematics with a B.A. degree from Carnegie Mellon University in 1970.[1]

From 1972 to 1973, he was a research and teaching assistant at Ohio State University, where he earned the Master of Science degree in Mathematics.[1]

In 1976, he went to work at Wayne State University, where he concentrated the research on chromatic numbers and Brooks' theorem. As a result, Paul A. Catlin published one of the most cited papers in that series: Hajós graph coloring conjecture: variations and counterexamples.,[1][7] which showed that the conjecture raised by Hugo Hadwiger is further strenghtened not only by but also by ,[8] which led to the joint paper written with Paul Erdős and Béla Bollobás entitled Hadwiger's conjecture is true for almost every graph.[5]

Published academic papers

  • Paul A. Catlin; Hong-Jian Lai; Yehong Shao (2009). "Edge-connectivity and edge-disjoint spanning trees". Discrete Mathematics. 309 (5): 1033–1040. doi:10.1016/j.disc.2007.11.056.
  • Paul A. Catlin; Arthur M. Hobbs; Hong-jian Lai (2001). "Graph family operations". Discrete Mathematics. 230 (1–3): 71–97. doi:10.1016/S0012-365X(00)00071-6.
  • Paul Catlin; Arthur M. Hobbs; Hong-Jian Lai; Neil Robertson (2001). "Preface: Paul Catlin 1948-1995". Journal of Sound and Vibration.
  • Paul A. Catlin; S. Brownsellt; D. A. Bradley; R. Bragg; J. Carlier (1999). Do users want telecare and can it be cost-effective. Annual International Conference of the IEEE Engineering in Medicine and Biology Society. Vol. 2. doi:10.1109/IEMBS.1999.803869.
  • Paul A. Catlin (1977). "Embedding subgraphs under extremal degree conditions" (PDF). Congressus Numerantium. 19: 136–45.
  • Paul A. Catlin; Zheng-yiao Han; Hong-jian Lai (1996). "Graphs without spanning closed trails". Discrete Mathematics. 160 (1–3): 81–91. doi:10.1016/S0012-365X(95)00149-Q.
  • Paul A. Catlin (1996). "The reduction of graph families closed under contraction". Discrete Mathematics. 160 (1–3): 67–80. doi:10.1016/0012-365X(95)00150-U.
  • Paul A. Catlin (1970). "Concerning the iterated function" (PDF). American Mathematical Monthly. 77 (1): 60–61.
  • Paul A. Catlin (1974). "On the divisors of second-order recurrence" (PDF). The Fibonacci Quaterly. 12 (2).
  • Paul A. Catlin (1974). "Lower bound for the period of the Fibonacci series modulo " (PDF). The Fibonacci Quaterly. 12 (4): 349–50.
  • Paul A. Catlin (1974). "On the multiplication of recurrences" (PDF). The Fibonacci Quaterly. 12: 365–68.
  • Paul A. Catlin (1990). "Graphs without nontrivial collapsible subgraphs" (PDF). Congressus Numerantium. 74: 233–38.
  • Paul A. Catlin; Hong-jian Lai (1996). "Supereulerian Graphs and the Petersen Graph". Journal of Combinatorial Theory. 66 (1): 123–139. doi:10.1006/jctb.1996.0009.
  • Paul A. Catlin (1979). "Hajós' graph-coloring conjecture: Variations and counterexamples" (PDF). Journal of Combinatorial Theory. 26 (2): 268–274. doi:10.1016/0095-8956(79)90062-5.
  • Paul A. Catlin (1979). "Brooks' graph-coloring theorem and the independence number". Journal of Combinatorial Theory. 27 (1): 42–48.
  • Paul A. Catlin (1996). "A reduction criterion for super-Eulerian graphs". Journal of Graph Theory. 22 (2): 151–153. doi:10.1002/(SICI)1097-0118(199606)22:2<151::AID-JGT5>3.0.COand2-M.
  • Catlin, Paul A. (1991). "Spanning trails joining two given edges". In Alavi, Yousef; Schwenk, Allen; Chartrand, G (eds.). Graph Theory, Combinatorics, and Applications (PDF). Wiley and Sons, Inc. pp. 207–22.
  • Paul A. Catlin; Hong-jian Lai (1995). "Vertex arboricity and maximum degree" (PDF). Discrete Mathematics. 141 (1–3): 37–46. doi:10.1016/0012-365X(93)E0205-I.
  • Catlin, Paul A. (1991). "Chapter 10: The arboricity of the random graph". In Alavi, Yousef (ed.). Graph theory, combinatorics, algorithms, and applications. Society for Industrial and Applied Mathematics. ISBN 0898712874. {{cite book}}: More than one of |first1= and |first= specified (help); More than one of |last1= and |last= specified (help)
  • Paul A. Catlin (1992). "Super-Eulerian graphs: A survey". Journal of Graph Theory. 16 (2): 177–196. doi:10.1002/jgt.3190160209.
  • Paul A. Catlin; Arthur M. Hobbs; Hong-jian Lai (1992). "Fractional Arboricity Strength and Principal Partitions in Graphs and Matroids". Discrete Applied Mathematics. 40 (3): 285–302. doi:10.1016/0166-218X(92)90002-R. {{cite journal}}: More than one of |author1= and |author= specified (help)
  • Paul A. Catlin (1978). "Nonisomorphic graphs having the same vertex neighborhood family". Congressus Numerantium. 21: 189–93.
  • Catlin, Paul A. (1991). "Chapter 7: Non-super-Eulerian graphs with large size". In Y. Alavi (ed.). Graph theory, combinatorics, algorithms, and applications (PDF). pp. 83–95. {{cite book}}: More than one of |first1= and |first= specified (help); More than one of |last1= and |last= specified (help)
  • Paul A. Catlin; T. N. Janakiraman Iqbalunnisa; N. Srinivasan (1990). "Hamilton cycles and closed trails in iterated line graphs" (PDF). Journal of Graph Theory. 14 (3): 347–364. doi:10.1002/jgt.3190140308.
  • Paul A. Catlin (1989). "Double cycle covers and the petersen graph". Journal of Graph Theory. 13 (4): 465–483. doi:10.1002/jgt.3190130408.
  • Paul A. Catlin (1989). "Spanning Eulerian subgraphs and matchings". Discrete Mathematics. 76 (2): 95–116. doi:10.1016/0012-365X(89)90303-8.
  • Paul A. Catlin (1988). "A reduction method to find spanning Eulerian subgraphs" (PDF). Journal of Graph Theory. 12 (1): 29–44. doi:10.1002/jgt.319012010.
  • Paul A. Catlin (1988). "Contractions of graphs with no spanning Eulerian subgraphs". Combinatorica. 8 (4): 313–321. doi:10.1007/BF02189088.
  • Paul A. Catlin (1988). "Graph homomorphisms into the five-cycle". Journal of Combinatorial Theory. 45 (2): 199–211. doi:10.1016/0095-8956(88)90069-X.
  • Paul A. Catlin; Michael O. Albertson; Luana Gibbons (1985). "Homomorphisms of 3-chromatic graphs, II" (PDF): 19–28. {{cite journal}}: Cite journal requires |journal= (help)
  • Paul A. Catlin (1987). "Spanning trails". Journal of Graph Theory. 11 (2): 161–167. doi:10.1002/jgt.3190110206.
  • Paul A. Catlin (1987). "Super-Eulerian graphcollapsible graphs, and four-cycles" (PDF). Congressus Numerantium. 58: 233–46.
  • Paul A. Catlin (1988). "Nearly-Eulerian spanning subgraphs" (PDF). Ars Combinatoria. 25: 115–24.
  • Béla Bollobás; Paul A. Catlin (1981). "Topological cliques of random graphs". Journal of Combinatorial Theory. 30 (2): 224–227. doi:10.1016/0095-8956(81)90066-6.
  • Paul A. Catlin (1979). "Brooks' graph-coloring theorem and the independence number". Journal of Combinatorial Theory. 27 (1): 42–48. doi:10.1016/0095-8956(79)90066-2.
  • P Catlin (1979). "Subgraphs with triangular components". Discrete Mathematics. 27 (2): 149–170. doi:10.1016/0012-365X(79)90106-7.
  • Paul A. Catlin (1979). "Survey Of Extensions Of Brooks' Graph Coloring Theorem". Annals of The New York Academy of Sciences. 328 (1 Topics i): 95–99. doi:10.1111/j.1749-6632.1979.tb17770.x.
  • Paul A. Catlin (1985). "Homomorphisms as a generalization of graph coloring" (PDF). Congressus Numerantium. 50: 179–86.
  • P. A. Catlin (1978). "A bound on the chromatic number of a graph". Discrete Mathematics. 22 (1): 81–83. doi:10.1016/0012-365X(78)90049-3.
  • Paul A. Catlin (1978). "Another bound on the chromatic number of a graph". Discrete Mathematics. 24 (1): 1–6. doi:10.1016/0012-365X(78)90167-X.
  • Paul A. Catlin (1978). "Graph Decompositions Satisfying Extremal Degree Constraints". Journal of Graph Theory. 2 (2): 165–170. doi:10.1002/jgt.3190020210.
  • Paul A. Catlin (1990). "Double cycle covers and the Petersen graph, II". Congressus Numerantium. 74: 233–38.
  • Paul A. Catlin (1976). "Two problems in metric diophantine approximation I". Journal of Number Theory. 8 (3): 282–288. doi:10.1016/0022-314X(76)90006-8.
  • Paul A. Catlin (1976). "Two problems in metric diophantine approximation II". Journal of Number Theory. 8 (3): 289–297. doi:10.1016/0022-314X(76)90007-X.
  • Paul A. Catlin; Béla Bollobás; Paul Erdős (1980). "Hadwiger's conjecture is true for almost every graph" (PDF). European Journal of Combinatorics.
  • Paul A. Catlin (1974). "Subgraphs of graphs I". Discrete Mathematics. 10 (2): 225–233. doi:10.1016/0012-365X(74)90119-8.
  • Paul A. Catlin; Arthur M. Hobbs; Hong-Jian Lai (2001). "Graph family operations". Discrete Mathematics. 230 (1–3): 71–97.

References

  1. ^ a b c d e f Hobbs, Arthur M.; Lai, Hong-Jian; Robertson, Neil (2001). "Paul Catlin 1948–1995". Discrete Mathematics. 230 (1–3): 3–12. {{cite journal}}: |chapter= ignored (help)
  2. ^ "List of publications of Paul A. Catlin". Leibniz Center for Informatics.
  3. ^ a b "Publications of Paul A. Catlin". West Virginia Universiy.
  4. ^ a b "Coauthor index". Leibniz Center for Informatics.
  5. ^ a b Paul A. Catlin; Béla Bollobás; Paul Erdős (1980). "Hadwiger's conjecture is true for almost every graph" (PDF). European Journal of Combinatorics.
  6. ^ Catlin, Paul A (1976). Embedding subgraphs and coloring graphs under extremal degree conditions (PDF) (Ph.D.). Ohio State University.
  7. ^ Paul A. Catlin (1979). "Hajós' graph-coloring conjecture: Variations and counterexamples" (PDF). Journal of Combinatorial Theory. 26 (2): 268–274. doi:10.1016/0095-8956(79)90062-5.
  8. ^ Hadwiger's conjecture generalizations

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