The relaxed game chromatic index of k-degenerate graphs

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 Delta(G) = Delta, then the first player, Alice, has a winning strategy for this game with r = Delta + k - 1 and d >=> 2k(2) + 4k. (C) 2006 Elsevier B.V. All rights reserved.