Jump to content

Paul A. Catlin: Difference between revisions

From Wikipedia, the free encyclopedia
Browse history interactively
← Previous edit
Content deleted Content added
VisualWikitext
7cc.19edv (talk | contribs)
271 edits
mNo edit summary
 
(38 intermediate revisions by 22 users not shown)
Line 1: Line 1:
{{short description|American mathematician}}
'''Paul Allen Catlin''' ({{dob|1948|6|25}} - {{Date of death|1995|4|20}}) was a mathematician, Doctor of Mathematics, and professor of Mathematics, known for his valuable contributions to [[Graph Theory]] and [[Number Theory]]. <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>
{{primary sources|date=September 2021}}
{{Infobox scientist
| name = Paul Allen Catlin
| image = <!--(as myimage.jpg, no 'File:')-->
| image_size =
| alt =
| caption =
| birth_date = {{Birth date|1948|6|25}}
| birth_place =
| death_date = {{Death date and age|1995|4|20|1948|6|25}}
| death_place =
| resting_place =
| resting_place_coordinates = <!-- {{Coord|LAT|LONG|type:landmark|display=inline,title}} -->
| residence =
| citizenship =
| nationality =
| fields = [[Mathematics]]
| workplaces =
| alma_mater = [[Ohio State University]]
| thesis_title = Embedding subgraphs and coloring graphs under extremal degree conditions
| thesis_url =
| thesis_year = 1976
| doctoral_advisor = [[Neil Robertson (mathematician)|G. Neil Robertson]]
| academic_advisors =
| doctoral_students =
| notable_students =
| known_for = [[Graph theory]]<br/>[[Number theory]]
| author_abbrev_bot =
| author_abbrev_zoo =
| influences =
| influenced =
| awards =
| signature = <!--(filename only)-->
| signature_alt =
| website = <!-- {{URL|www.example.com}} -->
| footnotes =
| spouse =
}}


'''Paul Allen Catlin''' ({{birth date|1948|6|25}} – {{Date of death|1995|4|20}}) was a mathematician, professor of mathematics who worked in [[graph theory]] and [[number theory]]. He wrote a significant paper on the series of chromatic numbers and Brooks' theorem, titled '' Hajós graph coloring conjecture: variations and counterexamples''.<ref name=catlin>{{cite journal |last1= Hobbs |first1= Arthur M. |author1-link= Arthur Hobbs (mathematician) |last2= Lai |first2= Hong-Jian |last3= Robertson |first3= Neil |authorlink3= Neil Robertson (mathematician) |title= Paul Catlin 1948–1995 |postscript= ; Preface pp. 3–6, |journal= Discrete Mathematics |year= 2001 |volume= 230 |issue= 1–3 |pages= 3–12 |url= http://www.math.wvu.edu/~hjlai/Pdf/Paul_Catlin.pdf |doi= 10.1016/s0012-365x(00)00065-0 |doi-access= free }} [http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/ListPublicationsCatlin.htm Publication list for Paul Catlin, math.wvu.edu] {{Webarchive|url=https://web.archive.org/web/20170809125550/http://www.math.wvu.edu/~hjlai/Pdf//Paul_Catlin.pdf |date=2017-08-09 }}</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 University |access-date=2012-10-25 |archive-url=https://web.archive.org/web/20170809125550/http://www.math.wvu.edu/~hjlai/Pdf//Paul_Catlin.pdf |archive-date=2017-08-09 |url-status=dead }}</ref>
'''Paul Allen Catlin''' 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
|author2 = Béla Bollobás
|author3 = Paul Erdős
|title = Hadwiger’s conjecture is true for almost every graph
|journal= European Journal of Combinatorics
|year= 1980
|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/>


==Career==
Originally from [[Bridgeport]], [[Connecticut]], '''Paul A. Catlin''' 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/>
Originally from [[Bridgeport]], [[Connecticut]], Catlin majored in Mathematics with a B.A. degree from [[Carnegie Mellon University]] in 1970.<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
Catlin held a Doctorate in Mathematics degree from [[Ohio State University]]. 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, Catlin published a significant paper 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
Line 21: Line 53:
|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
|url= http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin14.pdf
|url= http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin14.pdf
|doi-access = free
}} </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 strengthened not only by <math> k \le 4 </math> but also by <math> k \ge 7 </math>, which led to the joint paper written with [[Paul Erdős]] and [[Béla Bollobás]] titled ''Hadwiger's conjecture is true for almost every graph''.<ref name=hadwiger/>


He 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 Quarterly]]'', 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 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
==Published academic papers==
|author = Paul A. Catlin
|author2 = Béla Bollobás
|author3 = Paul Erdős
|title = Hadwiger's conjecture is true for almost every graph
|journal = European Journal of Combinatorics
|volume = 1
|issue = 3
|pages = 195
|year = 1980
|doi = 10.1016/s0195-6698(80)80001-1
|doi-access =
}}</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>




==Selected publications==
==References==
{{reflist}}


* {{cite journal
<!-- Metadata: see [[Wikipedia:Persondata]] -->
|author = Paul A. Catlin
{{Persondata
|author2= Hong-Jian Lai
| NAME = Catlin, Paul Allen
|author3= Yehong Shao
| ALTERNATIVE NAMES = Catlin, Paul
|title = Edge-connectivity and edge-disjoint spanning trees
| SHORT DESCRIPTION = Mathematician
|journal = Discrete Mathematics
| DATE OF BIRTH = June 25, 1948
|volume = 309
| PLACE OF BIRTH = [[Bridgeport]] [[Connecticut]]
|year = 2009
| DATE OF DEATH = April 20, 1995
|pages = 1033–1040
| PLACE OF DEATH = [[Detroit]] [[Michigan]]
|issue = 5
|doi = 10.1016/j.disc.2007.11.056
|doi-access =
}}
* {{cite journal
|author = Paul A. Catlin
|author2= Arthur M. Hobbs
|author3= Hong-jian Lai
|title = Graph family operations
|journal = Discrete Mathematics
|volume = 230
|year = 2001
|pages = 71–97
|issue = 1–3
|doi = 10.1016/S0012-365X(00)00071-6
|doi-access =
}}
}}
* {{cite journal
|author = Paul Catlin
|author2= Arthur M. Hobbs
|author3= Hong-Jian Lai
|author4= Neil Robertson
|title = Preface: Paul Catlin 1948-1995
|journal = Journal of Sound and Vibration
|year = 2001
}}
* {{cite conference
|author = Paul A. Catlin
|author2= S. Brownsellt
|author3= D. A. Bradley
|author4= R. Bragg
|author5= J. Carlier
|title= Proceedings of the First Joint BMES/EMBS Conference. 1999 IEEE Engineering in Medicine and Biology 21st Annual Conference and the 1999 Annual Fall Meeting of the Biomedical Engineering Society (Cat. No.99CH37015)
|chapter = Do users want telecare and can it be cost-effective
|conference = Annual International Conference of the IEEE Engineering in Medicine and Biology Society
|volume = 2
|year = 1999
|page= 714
|doi = 10.1109/IEMBS.1999.803869
|isbn= 0-7803-5674-8
}}
* {{cite journal
|author = Paul A. Catlin
|title = Embedding subgraphs under extremal degree conditions
|journal = Congressus Numerantium
|year = 1977
|volume = 19
|pages = 136–45
|url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin08.pdf
}}
* {{cite journal
|author = Paul A. Catlin
|author2= Zheng-yiao Han
|author3= Hong-jian Lai
|title = Graphs without spanning closed trails
|journal = Discrete Mathematics
|volume = 160
|year = 1996
|pages = 81–91
|issue = 1–3
|doi = 10.1016/S0012-365X(95)00149-Q
|doi-access =
}}
* {{cite journal
|author = Paul A. Catlin
|title = The reduction of graph families closed under contraction
|journal = Discrete Mathematics
|volume = 160
|year = 1996
|pages = 67–80
|issue = 1–3
|doi = 10.1016/0012-365X(95)00150-U
|doi-access = free
}}
* {{cite journal
|author= Paul A. Catlin
|title= Concerning the iterated <math>\phi</math> function
|journal= American Mathematical Monthly
|year= 1970
|volume= 77
|issue= 1
|pages= 60–61
|url= http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin01.pdf
|doi=10.2307/2316857
|jstor= 2316857
}}
* {{cite journal
|author= Paul A. Catlin
|title= On the divisors of second-order recurrence
|journal= The Fibonacci Quarterly
|year= 1974
|volume= 12
|issue= 2
|url= http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin02.pdf
}}
* {{cite journal
|author= Paul A. Catlin
|title= Lower bound for the period of the Fibonacci series modulo <math>m</math>
|journal= The Fibonacci Quarterly
|year= 1974
|volume = 12
|issue= 4
|pages= 349–50
|url= http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin03.pdf
}}
* {{cite journal
|author= Paul A. Catlin
|title= On the multiplication of recurrences
|journal = The Fibonacci Quarterly
|year = 1974
|volume= 12
|pages = 365–68
|url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin04.pdf
}}
* {{cite journal
|author = Paul A. Catlin
|title = Graphs without nontrivial collapsible subgraphs
|journal = Congressus Numerantium
|year = 1990
|volume = 74
|pages = 233–38
|url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin35.pdf
}}
* {{cite journal
|author = Paul A. Catlin
|author2= Hong-jian Lai
|title = Supereulerian Graphs and the Petersen Graph
|journal = Journal of Combinatorial Theory
|volume = 66
|year = 1996
|pages = 123–139
|issue = 1
|doi = 10.1006/jctb.1996.0009
|doi-access = free
}}
* {{cite journal
|author = Paul A. Catlin
|title = Hajós' graph-coloring conjecture: Variations and counterexamples
|journal = Journal of Combinatorial Theory
|volume = 26
|year = 1979
|pages = 268–274
|issue = 2
|doi = 10.1016/0095-8956(79)90062-5
|url= http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin14.pdf
|doi-access = free
}}
* {{cite journal
|author= Paul A. Catlin
|title= Brooks' graph-coloring theorem and the independence number
|journal = Journal of Combinatorial Theory
|volume = 27
|year = 1979
|issue = 1
|pages = 42–48
|doi=10.1016/0095-8956(79)90066-2
|doi-access = free
}}
* {{cite journal
|author = Paul A. Catlin
|title = A reduction criterion for super-Eulerian graphs
|journal = Journal of Graph Theory
|volume = 22
|year = 1996
|pages = 151–153
|issue = 2
|doi = 10.1002/(sici)1097-0118(199606)22:2<151::aid-jgt5>3.0.co;2-m
}}
* {{cite book
|last = Catlin
|first = Paul A.
|editor-last = Alavi
|editor-first = Yousef
|editor2-last = Schwenk
|editor2-first = Allen
|editor3-last = Chartrand
|editor3-first = G
|title = Graph Theory, Combinatorics, and Applications
|chapter = Spanning trails joining two given edges
|year = 1991
|publisher = Wiley and Sons, Inc.
|pages = 207–22
|chapter-url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin38.pdf
}}
* {{cite journal
|author = Paul A. Catlin
|author2= Hong-jian Lai
|title = Vertex arboricity and maximum degree
|journal = Discrete Mathematics
|volume = 141
|year = 1995
|pages = 37–46
|issue = 1–3
|doi = 10.1016/0012-365X(93)E0205-I
|url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin46.pdf
|doi-access = free
}}
* {{cite book
|last1 = Catlin
|first1 = Paul A.
|last2 = Chen
|first2 = Zhi-Hong
|chapter = Chapter 10: The arboricity of the random graph
|title = Graph theory, combinatorics, algorithms, and applications.
|editor-last = Alavi
|editor-first = Yousef
|editor-link = Yousef Alavi
|year = 1991
|publisher = Society for Industrial and Applied Mathematics
|isbn = 978-0898712872
}}
* {{cite journal
|author = Paul A. Catlin
|title = Super-Eulerian graphs: A survey
|journal = Journal of Graph Theory
|volume = 16
|year = 1992
|pages = 177–196
|issue = 2
|doi = 10.1002/jgt.3190160209
|citeseerx = 10.1.1.385.2901
}}
* {{cite journal
|author = Paul A. Catlin
|author2 = Jerrold W. Grossman
|author3 = Arthur M. Hobbs
|author4 = Hong-jian Lai
|title = Fractional Arboricity Strength and Principal Partitions in Graphs and Matroids
|journal = Discrete Applied Mathematics
|volume = 40
|year = 1992
|pages = 285–302
|issue = 3
|doi = 10.1016/0166-218X(92)90002-R
|doi-access =
}}
* {{cite journal
|author = Paul A. Catlin
|title = Nonisomorphic graphs having the same vertex neighborhood family
|journal= Congressus Numerantium
|volume = 21
|year = 1978
|pages = 189–93
}}
* {{cite book
|last1 = Catlin
|first1 = Paul A.
|last2 = Chen
|first2 = Zhi-Hong
|editor = Y. Alavi
|chapter = Chapter 7: Non-super-Eulerian graphs with large size
|title = Graph theory, combinatorics, algorithms, and applications
|year = 1991
|pages = 83–95
|chapter-url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin39.pdf
}}
* {{cite journal
|author = Paul A. Catlin
|author2= T. N. Janakiraman Iqbalunnisa
|author3= N. Srinivasan
|title = Hamilton cycles and closed trails in iterated line graphs
|journal = Journal of Graph Theory
|volume = 14
|year = 1990
|pages = 347–364
|issue = 3
|doi = 10.1002/jgt.3190140308
|url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin34a.pdf
|citeseerx= 10.1.1.385.3357
}}
* {{cite journal
|author = Paul A. Catlin
|title = Double cycle covers and the petersen graph
|journal = Journal of Graph Theory
|volume = 13
|year = 1989
|pages = 465–483
|issue = 4
|doi = 10.1002/jgt.3190130408
}}
* {{cite journal
|author = Paul A. Catlin
|title = Spanning Eulerian subgraphs and matchings
|journal = Discrete Mathematics
|volume = 76
|year = 1989
|pages = 95–116
|issue = 2
|doi = 10.1016/0012-365X(89)90303-8
|doi-access = free
}}
* {{cite journal
|author = Paul A. Catlin
|title = A reduction method to find spanning Eulerian subgraphs
|journal = Journal of Graph Theory
|volume = 12
|year = 1988
|pages = 29–44
|issue = 1
|doi = 10.1002/jgt.3190120105
|url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin26.pdf
}}
* {{cite journal
|author = Paul A. Catlin
|title = Contractions of graphs with no spanning Eulerian subgraphs
|journal = Combinatorica
|volume = 8
|year = 1988
|pages = 313–321
|issue = 4
|doi = 10.1007/BF02189088
|s2cid = 30831342
}}
* {{cite journal
|author = Paul A. Catlin
|title = Graph homomorphisms into the five-cycle
|journal = Journal of Combinatorial Theory
|volume = 45
|year = 1988
|pages = 199–211
|issue = 2
|doi = 10.1016/0095-8956(88)90069-X
|doi-access = free
}}
* {{cite journal
|author= Paul A. Catlin
|author2= Michael O. Albertson
|author3= Luana Gibbons
|title= Homomorphisms of 3-chromatic graphs, II
|year= 1985
|pages= 19–28
|url= http://carbon.ucdenver.edu/~egethner/MikeAlbertson/Papers/AlbertsonCatlin_Homom3ChromaticII_1985.pdf
}}
* {{cite journal
|author = Paul A. Catlin
|title = Spanning trails
|journal = Journal of Graph Theory
|volume = 11
|year = 1987
|pages = 161–167
|issue = 2
|doi = 10.1002/jgt.3190110206
}}
* {{cite journal
|author= Paul A. Catlin
|title= Super-Eulerian graphcollapsible graphs, and four-cycles
|journal= Congressus Numerantium
|volume= 58
|year= 1987
|pages= 233–46
|url= http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin23.pdf
}}
* {{cite journal
|author= Paul A. Catlin
|title = Nearly-Eulerian spanning subgraphs
|journal = Ars Combinatoria
|volume = 25
|year = 1988
|pages = 115–24
|url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin24.pdf
}}
* {{cite journal
|author = Béla Bollobás
|author2= Paul A. Catlin
|title = Topological cliques of random graphs
|journal = Journal of Combinatorial Theory
|volume = 30
|year = 1981
|pages = 224–227
|issue = 2
|doi = 10.1016/0095-8956(81)90066-6
|doi-access =
}}
* {{cite journal
|author = Paul A. Catlin
|title = Brooks' graph-coloring theorem and the independence number
|journal = Journal of Combinatorial Theory
|volume = 27
|year = 1979
|pages = 42–48
|issue = 1
|doi = 10.1016/0095-8956(79)90066-2
|doi-access = free
}}
* {{cite journal
|author = P Catlin
|title = Subgraphs with triangular components
|journal = Discrete Mathematics
|volume = 27
|year = 1979
|pages = 149–170
|issue = 2
|doi = 10.1016/0012-365X(79)90106-7
|doi-access = free
}}
* {{cite journal
|author = Paul A. Catlin
|title = Survey Of Extensions Of Brooks' Graph Coloring Theorem
|journal = Annals of the New York Academy of Sciences
|volume = 328
|year = 1979
|pages = 95–99
|issue = 1 Topics i
|doi = 10.1111/j.1749-6632.1979.tb17770.x
|bibcode = 1979NYASA.328...95C
|s2cid = 85819734
}}
* {{cite journal
|author = Paul A. Catlin
|title = Homomorphisms as a generalization of graph coloring
|journal = Congressus Numerantium
|volume = 50
|year = 1985
|pages = 179–86
|url = http://www.math.wvu.edu/~hjlai/Pdf/Catlin_Pdf/Catlin21.pdf
}}
* {{cite journal
|author = P. A. Catlin
|title = A bound on the chromatic number of a graph
|journal = Discrete Mathematics
|volume = 22
|year = 1978
|pages = 81–83
|issue = 1
|doi = 10.1016/0012-365X(78)90049-3
|doi-access = free
}}
* {{cite journal
|author = Paul A. Catlin
|title = Another bound on the chromatic number of a graph
|journal = Discrete Mathematics
|volume = 24
|year = 1978
|pages = 1–6
|issue = 1
|doi = 10.1016/0012-365X(78)90167-X
|doi-access = free
}}
* {{cite journal
|author = Paul A. Catlin
|title = Graph Decompositions Satisfying Extremal Degree Constraints
|journal = Journal of Graph Theory
|volume = 2
|year = 1978
|pages = 165–170
|issue = 2
|doi = 10.1002/jgt.3190020210
}}
* {{cite journal
|author = Paul A. Catlin
|title = Double cycle covers and the Petersen graph, II
|journal = Congressus Numerantium
|volume = 74
|year = 1990
|pages = 233–38
}}
* {{cite journal
|author = Paul A. Catlin
|title = Two problems in metric diophantine approximation I
|journal = Journal of Number Theory
|volume = 8
|year = 1976
|pages = 282–288
|issue = 3
|doi = 10.1016/0022-314X(76)90006-8
|doi-access = free
}}
* {{cite journal
|author = Paul A. Catlin
|title = Two problems in metric diophantine approximation II
|journal = Journal of Number Theory
|volume = 8
|year = 1976
|pages = 289–297
|issue = 3
|doi = 10.1016/0022-314X(76)90007-X
|doi-access = free
}}
* {{cite journal
|author = Paul A. Catlin
|author2 = Béla Bollobás
|author3 = Paul Erdős
|title = Hadwiger's conjecture is true for almost every graph
|journal = European Journal of Combinatorics
|volume = 1
|issue = 3
|pages = 195
|year = 1980
|doi = 10.1016/s0195-6698(80)80001-1
|doi-access =
}}
* {{cite journal
|author = Paul A. Catlin
|title = Subgraphs of graphs I
|journal = Discrete Mathematics
|volume = 10
|year = 1974
|pages = 225–233
|issue = 2
|doi = 10.1016/0012-365X(74)90119-8
|doi-access =
}}
* {{cite journal
|author = Paul A. Catlin
|author2= Arthur M. Hobbs
|author3= Hong-Jian Lai
|title = Graph family operations
|journal = Discrete Mathematics
|year= 2001
|volume= 230
|issue= 1–3
|pages= 71–97
|doi=10.1016/S0012-365X(00)00071-6
|doi-access=
}}

==References==
{{reflist}}

{{Authority control}}


{{DEFAULTSORT:Catlin, Paul}}
{{DEFAULTSORT:Catlin, Paul}}
[[Category:1948 births]]
[[Category:1948 births]]
[[Category:1995 deaths]]
[[Category:1995 deaths]]
[[Category:Mathematicians]]
[[Category:20th-century American mathematicians]]
[[Category:American number theorists]]
[[Category:Graph theorists]]
[[Category:Ohio State University Graduate School alumni]]
[[Category:Wayne State University faculty]]

Latest revision as of 06:52, 6 May 2024

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 who worked in graph theory and number theory. He wrote a significant paper on the series of chromatic numbers and Brooks' theorem, titled Hajós graph coloring conjecture: variations and counterexamples.[1][2][3]

Career

[edit]

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

Catlin held a Doctorate in Mathematics degree from Ohio State University. 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, Catlin published a significant paper in that series: Hajós graph coloring conjecture: variations and counterexamples.,[1][4] which showed that the conjecture raised by Hugo Hadwiger is further strengthened not only by but also by , which led to the joint paper written with Paul Erdős and Béla Bollobás titled Hadwiger's conjecture is true for almost every graph.[5]

He authored over fifty academic papers in number theory and graph theory. Many of his contributions and collaborations have been published in The Fibonacci Quarterly, in The Journal of Number Theory, in the Journal of Discrete Mathematics, and many other academic publications.[3] He co-authored scholarly papers with Arthur M. Hobbs,[6] Béla Bollobás and Paul Erdős,[5] Hong-Jian Lai, Zheng-Yiao Han, and Yehong Shao,[6] among others. He also published papers with G. Neil Robertson, with whom he also completed his dissertation thesis in 1976.[1][7]


Selected publications

[edit]

References

[edit]
  1. ^ a b c d e Hobbs, Arthur M.; Lai, Hong-Jian; Robertson, Neil (2001). "Paul Catlin 1948–1995" (PDF). Discrete Mathematics. 230 (1–3): 3–12. doi:10.1016/s0012-365x(00)00065-0; Preface pp. 3–6,{{cite journal}}: CS1 maint: postscript (link) Publication list for Paul Catlin, math.wvu.edu Archived 2017-08-09 at the Wayback Machine
  2. ^ "List of publications of Paul A. Catlin". Leibniz Center for Informatics.
  3. ^ a b "Publications of Paul A. Catlin" (PDF). West Virginia University. Archived from the original on 2017-08-09. Retrieved 2012-10-25.
  4. ^ 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.
  5. ^ a b Paul A. Catlin; Béla Bollobás; Paul Erdős (1980). "Hadwiger's conjecture is true for almost every graph". European Journal of Combinatorics. 1 (3): 195. doi:10.1016/s0195-6698(80)80001-1.
  6. ^ a b "Coauthor index". Leibniz Center for Informatics.
  7. ^ Catlin, Paul A (1976). Embedding subgraphs and coloring graphs under extremal degree conditions (PDF) (Ph.D.). Ohio State University.
Retrieved from "https://en.wikipedia.org/enwiki/w/index.php?title=Paul_A._Catlin&oldid=1222487733"