Discrete Mathematics and Combinatorics
The (r, d)-relaxed coloring game is a two-player game played on the vertex set of a graph G. We consider a natural analogue to this game on the edge set of G called the (r, d)-relaxed edge-coloring game. We consider this game on trees and more generally, on k-degenerate graphs. We show that if G is k-degenerate with ∆(G) = ∆, then the first player, Alice, has a winning strategy for this game with r = ∆+k−1 and d≥2k2 + 4k.
This is the author’s version of a work that was accepted for publication in Discrete Mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Discrete Mathematics, Volume 307, Issue 14, 2007, DOI: 10.1016/j.disc.2006.09.025
The Relaxed Game Chromatic Index of k-Degenerate Graphs.
Discrete Mathematics, 2007, volume 307, issue 14, pages 1767-1775
Dunn, Charles, "The Relaxed Game Chromatic Index of k-Degenerate Graphs" (2007). Faculty Publications. Accepted Version. Submission 1.