The Erdo{combining double acute accent}s-Hajnal conjecture for bull-free graphs

Maria Chudnovsky, Shmuel Safra

Research output: Contribution to journalArticle

24 Scopus citations

Abstract

The bull is a graph consisting of a triangle and two pendant edges. A graphs is called bull-free if no induced subgraph of it is a bull. In this paper we prove that every bull-free graph on n vertices contains either a clique or a stable set of size nfrac(1, 4), thus settling the Erdo{combining double acute accent}s-Hajnal conjecture [P. Erdo{combining double acute accent}s, A. Hajnal, Ramsey-type theorems, Discrete Appl. Math. 25 (1989) 37-52] for the bull.

Original languageEnglish (US)
Pages (from-to)1301-1310
Number of pages10
JournalJournal of Combinatorial Theory. Series B
Volume98
Issue number6
DOIs
StatePublished - Nov 1 2008
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

Keywords

  • Bull-free graphs
  • Clique
  • Induced subgraphs
  • Stable set

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