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

Maria Chudnovsky; Shmuel Safra

doi:10.1016/j.jctb.2008.02.005

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

Maria Chudnovsky, Shmuel Safra

Research output: Contribution to journal › Article › peer-review

42 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 n^{frac(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 language	English (US)
Pages (from-to)	1301-1310
Number of pages	10
Journal	Journal of Combinatorial Theory. Series B
Volume	98
Issue number	6
DOIs	https://doi.org/10.1016/j.jctb.2008.02.005
State	Published - Nov 2008
Externally published	Yes

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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10.1016/j.jctb.2008.02.005

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title = "The Erdo\{combining double acute accent\}s-Hajnal conjecture for bull-free graphs",

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.",

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AU - Safra, Shmuel

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N2 - 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.

AB - 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.

KW - Bull-free graphs

KW - Clique

KW - Induced subgraphs

KW - Stable set

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ER -

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

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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