Three-Coloring and List Three-Coloring of Graphs Without Induced Paths on Seven Vertices

Flavia Bonomo; Maria Chudnovsky; Peter Maceli; Oliver Schaudt; Maya Steinz; Mingxian Zhong

doi:10.1007/s00493-017-3553-8

Three-Coloring and List Three-Coloring of Graphs Without Induced Paths on Seven Vertices

Flavia Bonomo, Maria Chudnovsky, Peter Maceli, Oliver Schaudt, Maya Steinz, Mingxian Zhong

Mathematics

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

55 Scopus citations

Abstract

In this paper we present a polynomial time algorithm that determines if an input graph containing no induced seven-vertex path is 3-colorable. This affirmatively answers a question posed by Randerath, Schiermeyer and Tewes in 2002. Our algorithm also solves the list-coloring version of the 3-coloring problem, where every vertex is assigned a list of colors that is a subset of {1,2,3}, and gives an explicit coloring if one exists.

Original language	English (US)
Pages (from-to)	779-801
Number of pages	23
Journal	Combinatorica
Volume	38
Issue number	4
DOIs	https://doi.org/10.1007/s00493-017-3553-8
State	Published - Aug 1 2018

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics
Computational Mathematics

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abstract = "In this paper we present a polynomial time algorithm that determines if an input graph containing no induced seven-vertex path is 3-colorable. This affirmatively answers a question posed by Randerath, Schiermeyer and Tewes in 2002. Our algorithm also solves the list-coloring version of the 3-coloring problem, where every vertex is assigned a list of colors that is a subset of {1,2,3}, and gives an explicit coloring if one exists.",

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AU - Chudnovsky, Maria

AU - Maceli, Peter

AU - Schaudt, Oliver

AU - Steinz, Maya

AU - Zhong, Mingxian

PY - 2018/8/1

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AB - In this paper we present a polynomial time algorithm that determines if an input graph containing no induced seven-vertex path is 3-colorable. This affirmatively answers a question posed by Randerath, Schiermeyer and Tewes in 2002. Our algorithm also solves the list-coloring version of the 3-coloring problem, where every vertex is assigned a list of colors that is a subset of {1,2,3}, and gives an explicit coloring if one exists.

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Three-Coloring and List Three-Coloring of Graphs Without Induced Paths on Seven Vertices

Abstract

All Science Journal Classification (ASJC) codes

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