Faculty Publications
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
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
DigitalCommons@Linfield Citation
Dunn, Charles; Nordstrom, Jennifer Firkins; Naymie, Cassandra; Pitney, Erin; Sehorn, William; and Suer, Charlie, "Clique-Relaxed Graph Coloring" (2011). Faculty Publications. Published Version. Submission 4.
https://digitalcommons.linfield.edu/mathfac_pubs/4
Comments
This article is the publisher-created version, also considered to be the final version or the version of record. It includes value-added elements provided by the publisher, such as copy editing, layout changes, and branding consistent with the rest of the publication.