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The game of Col on complete k-ary trees

By Ro Cincotti and Timothée Bossart

Abstract

Abstract—Col is a classic combinatorial game played on graphs and to solve a general instance is a PSPACE-complete problem. However, winning strategies can be found for some specific graph instances. In this paper, the solution of Col on complete k-ary trees is presented. Keywords—Combinatorial game, Complete k-ary tree, Mapcoloring game. 1 he/she has a winning strategy without to be forced to paint the root. If First decides to play in one of the remaining n − 1 trees, then Second will do the same because, by induction hypothesis, he/she has a winning strategy in the remaining n−1 trees without to be forced to paint any root. An example is shown in Fig. 1. I

Year: 2011
OAI identifier: oai:CiteSeerX.psu:10.1.1.192.8295
Provided by: CiteSeerX
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