The cinderella game on holes and anti-holes

Authors:
Marijke H. L. Bodlaender;Cor A. J. Hurkens;Gerhard J. Woeginger
Affiliations:
Department of Information and Computing Sciences, Universiteit Utrecht, The Netherlands;Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands;Department of Mathematics and Computer Science, TU Eindhoven, The Netherlands
Venue:
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Year:
2011

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Abstract

We investigate a two-player game on graphs, where one player (Cinderella) wants to keep the behavior of an underlying water-bucket system stable whereas the other player (the wicked Stepmother) wants to cause overflows. The bucket number of a graph G is the smallest possible bucket size with which Cinderella can win the game. We determine the bucket numbers of all perfect graphs, and we also derive results on the bucket numbers of certain non-perfect graphs. In particular, we analyze the game on holes and (partially) on anti-holes for the cases where Cinderella sticks to a simple greedy strategy.