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2011 Clique-relaxed graph coloring
Charles Dunn, Jennifer Firkins Nordstrom, Cassandra Naymie, Erin Pitney, William Sehorn, Charlie Suer
Involve 4(2): 127-138 (2011). DOI: 10.2140/involve.2011.4.127

Abstract

We define a generalization of the chromatic number of a graph G called the k-clique-relaxed chromatic number, denoted χ(k)(G). We prove bounds on χ(k)(G) for all graphs G, including corollaries for outerplanar and planar graphs. We also define the k-clique-relaxed game chromatic number, χg(k)(G), of a graph G. We prove χg(2)(G)4 for all outerplanar graphs G, and give an example of an outerplanar graph H with χg(2)(H)3. Finally, we prove that if H is a member of a particular subclass of outerplanar graphs, then χg(2)(H)3.

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Charles Dunn. Jennifer Firkins Nordstrom. Cassandra Naymie. Erin Pitney. William Sehorn. Charlie Suer. "Clique-relaxed graph coloring." Involve 4 (2) 127 - 138, 2011. https://doi.org/10.2140/involve.2011.4.127

Information

Received: 27 August 2010; Revised: 10 February 2011; Accepted: 11 February 2011; Published: 2011
First available in Project Euclid: 20 December 2017

zbMATH: 1233.05101
MathSciNet: MR2876194
Digital Object Identifier: 10.2140/involve.2011.4.127

Subjects:
Primary: 05C15

Rights: Copyright © 2011 Mathematical Sciences Publishers

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Vol.4 • No. 2 • 2011
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