A coloring algorithm for 4K1-free line graphs

A coloring algorithm for 4K1-free line graphs

Given a family F of graphs, let Free (F) be the class of graphs that do not contain any member of F as an induced subgraph. When F is a set of four-vertex graphs the complexity of the vertex coloring problem in Free (F) is known, with three exceptions: F={claw,4K1}, F={claw,4K1,co-diamond}, and F={C...

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Veröffentlicht in:Discrete Applied Mathematics 2018-01, Vol.234, p.76-85
Hauptverfasser: Fraser, Dallas J., Hamel, Angèle M., Hoàng, Chính T., Maffray, Frédéric
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Claw
Computer Science
Discrete Mathematics
formula omitted
Graph coloring
Line-graph
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creator Fraser, Dallas J.
Hamel, Angèle M.
Hoàng, Chính T.
Maffray, Frédéric
description Given a family F of graphs, let Free (F) be the class of graphs that do not contain any member of F as an induced subgraph. When F is a set of four-vertex graphs the complexity of the vertex coloring problem in Free (F) is known, with three exceptions: F={claw,4K1}, F={claw,4K1,co-diamond}, and F={C4,4K1}. In this paper, we study the coloring problem for Free (claw, 4K1). We solve the vertex coloring problem for a subclass of Free (claw, 4K1) which contains the class of 4K1-free line graphs.
doi_str_mv 10.1016/j.dam.2017.06.006
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source Elsevier ScienceDirect Journals; EZB-FREE-00999 freely available EZB journals
subjects Claw
Computer Science
Discrete Mathematics
formula omitted
Graph coloring
Line-graph
title A coloring algorithm for 4K1-free line graphs
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