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The Relaxed Edge-Coloring Game And K-Degenerate Graphs, Charles Dunn, David Morawski, Jennifer Firkins Nordstrom
The Relaxed Edge-Coloring Game And K-Degenerate Graphs, Charles Dunn, David Morawski, Jennifer Firkins Nordstrom
Faculty Publications
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] …