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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.

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
2. Erdôs, P., Graph theory and probability, Can. J. Math. 11 (1959), 34–38.Google Scholar
3. Harary, F., Hedetniemi, S. T. and Robinson, R. W., Uniquely colourable graphs, J. Comb. Theory 6 (1969), 264–270.Google Scholar
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