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Uniquely Colourable Graphs with Large Girth

Published online by Cambridge University Press:  20 November 2018

Béla Bollobás  and
Norbert Sauer
Béla Bollobás
Affiliation:
University of Cambridge, Cambridge, England
Norbert Sauer
Affiliation:
University of Calgary, Calgary, Alberta
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Tutte [1], writing under a pseudonym, was the first to prove that a graph with a large chromatic number need not contain a triangle. The result was rediscovered by Zykov [5] and Mycielski [4]. Erdös [2] proved the much stronger result that for every k ≧ 2 and g there exist a k-chromatic graph whose girth is at least g.

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 6 , 01 December 1976 , pp. 1340 - 1344
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Descartes, B., A three colour problem, Eureka, April, 1947; Solution March, 1948.Google Scholar
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4. Mycielski, J., Sur le coloriage des graphes, Coll. Math. S (1955), 161–162.Google Scholar
5. Zykov, A. A., On some properties of linear complexes (in Russian), Mat. Sbornik, N.S. 24 (1949) 163–188. Amer. Math. Soc. Transi. 79 (1952).Google Scholar