The 2nd-order conditional 3-coloring of claw-free graphs
نویسندگان
چکیده
منابع مشابه
Dynamic 3-Coloring of Claw-free Graphs
A dynamic k-coloring of a graph G is a proper k-coloring of the vertices of G such that every vertex of degree at least 2 in G will be adjacent to vertices with at least 2 different colors. The smallest number k for which a graph G can have a dynamic k-coloring is the dynamic chromatic number, denoted by χd(G). In this paper, we investigate the dynamic 3-colorings of claw-free graphs. First, we...
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We prove that every claw-free graph G that does not contain a clique on ∆(G) ≥ 9 vertices can be ∆(G)− 1 colored.
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The 3-colorability problem is NP-complete in the class of clawfree graphs and it remains hard in many of its subclasses obtained by forbidding additional subgraphs. (Line graphs and claw-free graphs of vertex degree at most four provide two examples.) In this paper we study the computational complexity of the 3-colorability problem in subclasses of claw-free graphs defined by finitely many forb...
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We prove that if G is a quasi-line graph with ∆(G) > ω(G) and ∆(G) ≥ 69, then χOL(G) ≤ ∆(G) − 1. Together with our previous work, this implies that if G is a claw-free graph with ∆(G) > ω(G) and ∆(G) ≥ 69, then χl(G) ≤ ∆(G)− 1.
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Chudnovsky and Seymour proved that every connected claw-free graph that contains a stable set of size 3 has chromatic number at most twice its clique number. We improve this for small clique size, showing that every claw-free graph with clique number at most 3 is 4-choosable and every claw-free graph with clique number at most 4 is 7-choosable. These bounds are tight.
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2008
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2008.01.034