Coloring graphs with no induced five‐vertex path or gem

For a graph G, let χ(G) and ω(G), respectively, denote the chromatic number and clique number of G. We give an explicit structural description of (P5, gem)‐free graphs, and show that every such graph G satisfies χ(G)≤⌈5ω(G)4⌉. Moreover, this bound is best possible. Here a gem is the graph that consi...

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Bibliographic Details
Published in:	Journal of graph theory Vol. 95; no. 4; pp. 527 - 542
Main Authors:	Chudnovsky, Maria, Karthick, T., Maceli, Peter, Maffray, Frédéric
Format:	Journal Article
Language:	English
Published:	Hoboken Wiley Subscription Services, Inc 01-12-2020
Subjects:	Apexes chromatic number clique number Graphs P5‐free graphs χ‐boundedness
Online Access:	Get full text
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Summary:	For a graph G, let χ(G) and ω(G), respectively, denote the chromatic number and clique number of G. We give an explicit structural description of (P5, gem)‐free graphs, and show that every such graph G satisfies χ(G)≤⌈5ω(G)4⌉. Moreover, this bound is best possible. Here a gem is the graph that consists of an induced four‐vertex path plus a vertex which is adjacent to all the vertices of that path.
ISSN:	0364-9024 1097-0118
DOI:	10.1002/jgt.22572