Faculty Publications

Publication Date



Discrete Mathematics and Combinatorics


The (r, d)-relaxed edge-coloring game is a two-player game using r colors played on the edge set of a graph G. We consider this game on forests and more generally, on k-degenerate graphs. If F is a forest with ∆(F) = ∆, then the first player, Alice, has a winning strategy for this game with r = ∆ − j and d ≥ 2j + 2 for 0 ≤ j ≤ ∆ − 1. This both improves and generalizes the result for trees in [10]. More broadly, we generalize the main result in [10] by showing that if G is k-degenerate with ∆(G) = ∆ and j ∈ [∆ + k − 1], then there exists a function h(k, j) such that Alice has a winning strategy for this game with r = ∆ + kj and d ≥ h(k, j).

Document Type

Accepted Version


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).


The final publication is available at Springer via http://dx.doi.org/10.1007/s11083-014-9336-6.

Original Citation

Charles Dunn, David Morawski, & Jennifer Firkins Nordstrom
The relaxed edge-coloring game and k-degenerate graphs
Order, 2015, volume 32, issue 3, pages 347-361



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