Publication Date

2011

Disciplines

Discrete Mathematics and Combinatorics

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.

Document Type

Published Version

Comments

This article is the publisher-created published version.

Rights

Copyright ©2011 by Mathematical Sciences Publishers

Original Citation

Charles Dunn, Jennifer Firkins Nordstrom, Cassandra Naymie, Erin Pitney, William Sehorn, & Charlie Suer
Clique-relaxed graph coloring
Involve, 2011, volume 4, issue 2, pages 127-138
doi:10.2140/involve.2011.4.127

 
 

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