Game chromatic index of graphs with given restrictions on degrees

Given a graph G and an integer k, two players alternatively color the edges of G using k colors so that adjacent edges get different colors. The game chromatic index g(G) is the minimum k for which the first player has a strategy that ensures that all edges of G get colored. The trivial bounds are (G) g(G) 2(G) - 1, where (G) denotes the maximal degree of G. Lam, Shiu, and Xu and, independently, Bartnicki and Grytczuk asked whether there is a constant C such that g(G) (G) + C for every graph G. We show that the answer is in the negative by constructing graphs

• Type: Journal
• Year: 2008
• Where: TCS
• Authors: Andrew Beveridge, Tom Bohman, Alan M. Frieze, Oleg Pikhurko
• Keywords: Adjacent Edges, Game Chromatic Index, TCS 2008, Theoretical Computer Science, Trivial Bounds