Kayles and Nimbers

Kayles is a combinatorial game on graphs. Two players select alternatingly a vertex from a given graph G - a chosen vertex may not be adjacent or equal to an already chosen vertex. The last player that can select a vertex wins the game. The problem to determine which player has a winning strategy is known to be PSPACE-complete. Because of certain characteristics of the Kayles game, it can be analyzed with Sprague-Grundy theory. In this way, we can show that the problem is polynomial time solvable for graphs with a bounded asteroidal number. It is shown that the problem can be solved in O(n3) time on cocomparability graphs and circular arc graphs, and in

• Type: Journal
• Year: 2002
• Where: JAL
• Authors: Hans L. Bodlaender, Dieter Kratsch
• Keywords: Chosen Vertex, Combinatorial Game, Game, JAL 2002