Faculty Publications
Publication Date
2012
Disciplines
Discrete Mathematics and Combinatorics
Abstract
Let k be a positive integer, d be a nonnegative integer, and G be a finite graph. Two players, Alice and Bob, play a game on G by coloring the uncolored vertices with colors from a set X of k colors. At all times, the subgraph induced by a color class must have maximum degree at most d. Alice wins the game if all vertices are eventually colored; otherwise, Bob wins. The least k such that Alice has a winning strategy is called the d-relaxed game chromatic number of G, denoted χ gd (G). It is known that there exist graphs such that χ g0 (G) = 3, but χ g1 (G) > 3. We will show that for all positive integers m, there exists a complete multipartite graph G such that m ≤ χ g0 (G) < χ g1 (G).
Document Type
Accepted Version
Rights
This is an electronic version of an article published in Order, 2012, volume 29, issue 3, pages 507-512. Order is available online at: doi:10.1007/s11083-011-9217-1.
Original Citation
Charles Dunn
Complete multipartite graphs and the relaxed coloring game.
Order, 2012, volume 29, issue 3, pages 507-512
doi:10.1007/s11083-011-9217-1
DigitalCommons@Linfield Citation
Dunn, Charles, "Complete Multipartite Graphs and the Relaxed Coloring Game" (2012). Faculty Publications. Accepted Version. Submission 5.
https://digitalcommons.linfield.edu/mathfac_pubs/5
Comments
This article is the author-created version that incorporates referee comments. It is the accepted-for-publication version. The content of this version may be identical to the published version (the version of record) save for value-added elements provided by the publisher (e.g., copy editing, layout changes, or branding consistent with the rest of the publication).