On the Choosability of Claw-Free Perfect Graphs

It has been conjectured that for every claw-free graph G the choice number of G is equal to its chromatic number. We focus on the special case of this conjecture where G is perfect. Claw-free perfect graphs can be decomposed via clique-cutset into two special classes called elementary graphs and pec...

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Bibliographic Details
Published inGraphs and combinatorics Vol. 32; no. 6; pp. 2393 - 2413
Main Authors Gravier, Sylvain, Maffray, Frédéric, Pastor, Lucas
Format Journal Article
LanguageEnglish
Published Tokyo Springer Japan 01.11.2016
Springer Verlag
Subjects
Combinatorial analysis
Combinatorics
Computer Science
Decomposition
Discrete Mathematics
Engineering Design
Graphs
Mathematics
Mathematics and Statistics
Original Paper
List-coloring
Claw-free
Choosability
Perfect
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Summary:It has been conjectured that for every claw-free graph G the choice number of G is equal to its chromatic number. We focus on the special case of this conjecture where G is perfect. Claw-free perfect graphs can be decomposed via clique-cutset into two special classes called elementary graphs and peculiar graphs. Based on this decomposition we prove that the conjecture holds true for every claw-free perfect graph with maximum clique size at most 4.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:0911-0119
1435-5914
DOI:10.1007/s00373-016-1732-9