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

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-colorin...

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Bibliographic Details
Published in:Combinatorica (Budapest. 1981) Vol. 38; no. 4; pp. 779 - 801
Main Authors: Bonomo, Flavia, Chudnovsky, Maria, Maceli, Peter, Schaudt, Oliver, Stein, Maya, Zhong, Mingxian
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2018
Springer
Springer Nature B.V
Subjects:
Algorithms
Coloring
Combinatorics
Graph algorithms
Mathematics
Mathematics and Statistics
Set theory
05C85
05C15
05C37
ISSN:0209-9683, 1439-6912
Online Access:Get full text
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Summary: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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ISSN:0209-9683
1439-6912
DOI:10.1007/s00493-017-3553-8