Nearly bipartite graphs with large chromatic number
P. Erdős and A. Hajnal asked the following question. Does there exist a constant ε>0 with the following property: If every subgraphH of a graphG can be made bipartite by the omission of at most ε|H| edges where |H| denotes the number of vertices ofH thenx(H) ≦ 3.
The aim of this note is to give a negative answer to this question and consider the analogous problem for hypergraphs. The first was done also by L. Lovász who used a different construction.
AMS subject classification (1980)05 C 15 05 C 65
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