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On the chromatic number of subgraphs of a given graph

Author: V. Rödl
Journal: Proc. Amer. Math. Soc. 64 (1977), 370-371
MSC: Primary 05C15
MathSciNet review: 0469806
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Abstract: It is shown that for arbitrary positive integers m,n there exists a $\phi (m,n)$ such that if $\chi (G) \geqslant \phi (m,n)$, then G contains either a complete subgraph of size m or a subgraph H with $\chi (H) = n$ containing no ${C_3}$. This gives an answer to a problem of Erdös and Hajnal.

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Keywords: Graph, subgraph, triangle-free graph, chromatic number
Article copyright: © Copyright 1977 American Mathematical Society