Obstructions for three-coloring graphs without induced paths on six vertices

Maria Chudnovsky; Jan Goedgebeur; Oliver Schaudt; Mingxian Zhong

doi:10.1016/j.jctb.2019.04.006

Obstructions for three-coloring graphs without induced paths on six vertices

Maria Chudnovsky
, Jan Goedgebeur
, Oliver Schaudt
, Mingxian Zhong

Mathematics

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

14 Scopus citations

Abstract

We prove that there are 24 4-critical P₆-free graphs, and give the complete list. We remark that, if H is connected and not a subgraph of P₆, there are infinitely many 4-critical H-free graphs. Our result answers questions of Golovach et al. and Seymour.

Original language	English (US)
Pages (from-to)	45-83
Number of pages	39
Journal	Journal of Combinatorial Theory. Series B
Volume	140
DOIs	https://doi.org/10.1016/j.jctb.2019.04.006
State	Published - Jan 2020

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Discrete Mathematics and Combinatorics
Computational Theory and Mathematics

Keywords

Critical graph
Forbidden induced paths
Graph coloring

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10.1016/j.jctb.2019.04.006

Cite this

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title = "Obstructions for three-coloring graphs without induced paths on six vertices",

abstract = "We prove that there are 24 4-critical P6-free graphs, and give the complete list. We remark that, if H is connected and not a subgraph of P6, there are infinitely many 4-critical H-free graphs. Our result answers questions of Golovach et al. and Seymour.",

keywords = "Critical graph, Forbidden induced paths, Graph coloring",

author = "Maria Chudnovsky and Jan Goedgebeur and Oliver Schaudt and Mingxian Zhong",

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AU - Chudnovsky, Maria

AU - Goedgebeur, Jan

AU - Schaudt, Oliver

AU - Zhong, Mingxian

PY - 2020/1

Y1 - 2020/1

N2 - We prove that there are 24 4-critical P6-free graphs, and give the complete list. We remark that, if H is connected and not a subgraph of P6, there are infinitely many 4-critical H-free graphs. Our result answers questions of Golovach et al. and Seymour.

AB - We prove that there are 24 4-critical P6-free graphs, and give the complete list. We remark that, if H is connected and not a subgraph of P6, there are infinitely many 4-critical H-free graphs. Our result answers questions of Golovach et al. and Seymour.

KW - Critical graph

KW - Forbidden induced paths

KW - Graph coloring

UR - https://www.scopus.com/pages/publications/85067351414

UR - https://www.scopus.com/pages/publications/85067351414#tab=citedBy

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DO - 10.1016/j.jctb.2019.04.006

M3 - Article

AN - SCOPUS:85067351414

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VL - 140

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EP - 83

JO - Journal of Combinatorial Theory. Series B

JF - Journal of Combinatorial Theory. Series B

ER -

Obstructions for three-coloring graphs without induced paths on six vertices

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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