Induced Subgraphs of Graphs with Large Chromatic Number. III. Long Holes

Maria Chudnovsky; Alex Scott; Paul Seymour

doi:10.1007/s00493-016-3467-x

Induced Subgraphs of Graphs with Large Chromatic Number. III. Long Holes

Maria Chudnovsky, Alex Scott, Paul Seymour

Mathematics

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

22 Scopus citations

Abstract

We prove a 1985 conjecture of Gyárfás that for all k, ℓ, every graph with sufficiently large chromatic number contains either a clique of cardinality more than k or an induced cycle of length more than ℓ.

Original language	English (US)
Pages (from-to)	1057-1072
Number of pages	16
Journal	Combinatorica
Volume	37
Issue number	6
DOIs	https://doi.org/10.1007/s00493-016-3467-x
State	Published - Dec 1 2017

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Computational Mathematics

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title = "Induced Subgraphs of Graphs with Large Chromatic Number. III. Long Holes",

abstract = "We prove a 1985 conjecture of Gy{\'a}rf{\'a}s that for all k, ℓ, every graph with sufficiently large chromatic number contains either a clique of cardinality more than k or an induced cycle of length more than ℓ.",

author = "Maria Chudnovsky and Alex Scott and Paul Seymour",

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AU - Seymour, Paul

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N2 - We prove a 1985 conjecture of Gyárfás that for all k, ℓ, every graph with sufficiently large chromatic number contains either a clique of cardinality more than k or an induced cycle of length more than ℓ.

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JO - Combinatorica

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Induced Subgraphs of Graphs with Large Chromatic Number. III. Long Holes

Abstract

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