Clique-relaxed graph coloring

Charles Dunn, Jennifer Firkins Nordstrom, Cassandra Naymie, Erin Pitney, William Sehorn, Charlie Suer
2011 Involve. A Journal of Mathematics  
We define a generalization of the chromatic number of a graph G called the kclique-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, χ (k) g (G), of a graph G. We prove χ (2) g (G) ≤ 4 for all outerplanar graphs G, and give an example of an outerplanar graph H with χ (2) g (H ) ≥ 3. Finally, we prove that if H is a member of a particular
more » ... bclass of outerplanar graphs, then χ (2) g (H ) ≤ 3.
doi:10.2140/involve.2011.4.127 fatcat:626zgudu5fg4pal2puriu5ixf4