Geodesic
Uniquely Colourable Graphs with Large Girth
Canadian journal of mathematics, Tome 28 (1976) no. 6, pp. 1340-1344

Voir la notice de l'article provenant de la source Cambridge University Press

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. 
Bollobás, Béla; Sauer, Norbert. Uniquely Colourable Graphs with Large Girth. Canadian journal of mathematics, Tome 28 (1976) no. 6, pp. 1340-1344. doi: 10.4153/CJM-1976-133-5
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[1] 1. Descartes, B., A three colour problem, Eureka, April, 1947; Solution March, 1948. Google Scholar

[2] 2. Erdôs, P., Graph theory and probability, Can. J. Math. 11 (1959), 34–38. Google Scholar

[3] 3. Harary, F., Hedetniemi, S. T. and Robinson, R. W., Uniquely colourable graphs, J. Comb. Theory 6 (1969), 264–270. Google Scholar

[4] 4. Mycielski, J., Sur le coloriage des graphes, Coll. Math. S (1955), 161–162. Google Scholar

[5] 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

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