Kayles and Nimbers
نویسندگان
چکیده
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 O(n1+1/ log 3) = O(n1.631) time on cographs.
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ورودعنوان ژورنال:
- J. Algorithms
دوره 43 شماره
صفحات -
تاریخ انتشار 2002