The Erdős--Hajnal conjecture for bull-free graphs

  • Authors:

  • Maria Chudnovsky;Shmuel Safra

  • Affiliations:

  • Columbia University, New York, NY 10027, USA;Tel-Aviv University, Tel-Aviv, 69978, Israel

  • Venue:
  • Journal of Combinatorial Theory Series B
  • Year:
  • 2008

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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 n^1^4, thus settling the Erdos-Hajnal conjecture [P. Erdos, A. Hajnal, Ramsey-type theorems, Discrete Appl. Math. 25 (1989) 37-52] for the bull.