On coloring graphs with locally small chromatic number

H. A. Kierstead, E. Szemerédi, W. T. Trotter

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12 Citations (Scopus)

Abstract

In 1973, P. Erdös conjectured that for each kε2, there exists a constant c k so that if G is a graph on n vertices and G has no odd cycle with length less than c k n 1/k, then the chromatic number of G is at most k+1. Constructions due to Lovász and Schriver show that c k, if it exists, must be at least 1. In this paper we settle Erdös' conjecture in the affirmative. We actually prove a stronger result which provides an upper bound on the chromatic number of a graph in which we have a bound on the chromatic number of subgraphs with small diameter.

Original languageEnglish
Pages (from-to)183-185
Number of pages3
JournalCombinatorica
Volume4
Issue number2-3
DOIs
Publication statusPublished - Jun 1 1984

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Keywords

  • AMS subject classification (1980): 05C15

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Computational Mathematics

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