, Volume 2, Issue 4, pp 377–383 | Cite as

Nearly bipartite graphs with large chromatic number

  • Vojtěch Rödl


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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Copyright information

© Akadémiai Kiadó 1982

Authors and Affiliations

  • Vojtěch Rödl
    • 1
  1. 1.Dept. of MathematicsFJFI ČVUTPraha1 ČSSR

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