Paul Allen Catlin

from Wikipedia, the free encyclopedia

Paul Allen Catlin (born April 25, 1948 in Bridgeport , Connecticut , † April 20, 1995 in Detroit , Michigan ) was an American mathematician who dealt with graph theory and number theory.

Catlin was already very interested in mathematics as a schoolboy and built an adding machine out of relays when he was 14 . He studied at Carnegie Mellon University , where he published his first number theory work as an undergraduate . After completing his bachelor's degree in 1973, he studied at Ohio State University with a master's degree in 1975 and his doctorate in 1976 with Neil Robertson ( Embedding subgraphs and coloring graphs under extremal degree conditions ). Under Robertson he also turned to graph theory. As a post-graduate student , he went to Wayne State University . In 1981 he became an associate professor and later professor there.

Catlin extended R. Leonard Brooks' theorem on graph coloring. With Béla Bollobás and Paul Erdős he showed that Hadwinger's conjecture is correct for almost all graphs. He also found counterexamples for the tightening of Hadwinger's conjecture that György Hajós had formulated ( Hajós conjecture ).

In the 1980s, he introduced the concept of collapsible subgraph, which is fruitful for further research. He thus proved several results on Euler's subgraphs and Supereuler's graphs (those with factors that are Euler's graphs). In addition to graph theory, he dealt with number theory ( Diophantine approximations , Fibonacci sequences ).

His brother David W. Catlin is also a mathematician and professor at Purdue University .

Web links

Individual evidence

  1. ↑ A survey of extensions of Brook's graph coloring theorem. In: Frank Harary (Ed.): Topics in Graph Theory. Annals New York Academy of Science, Volume 329, 1979, pp. 95-99.
  2. ↑ Bollobas, Catlin, Erdős: Hadwiger's conjecture is true for almost every graph. European Journal of Combinatorics, Volume 1, 1980, pp. 195-199.
  3. ^ Catlin: Hajós' Graph-Coloring Conjecture: Variations and Counterexamples. J. Comb. Theory, B, Vol. 26, 1979, pp. 268-274.
  4. ↑ Catlin: Super-Eulerian graphs, collapsible graphs, and four-cycles. Congressus Numerantium, Volume 58, 1987, pp. 233-46.
  5. ↑ Spanning subgraphs, that is, with the same set of vertices as the graph.
  6. ^ E.g. Catlin: A reduction method to find spanning Eulerian subgraphs. J. Graph Theory 12 (1988) 29-44.
personal data
SURNAME Catlin, Paul Allen
BRIEF DESCRIPTION American mathematician
DATE OF BIRTH April 25, 1948
PLACE OF BIRTH Bridgeport , Connecticut
DATE OF DEATH April 20, 1995
Place of death Detroit , Michigan