Article
Strong reducibility of powers of paths and powers of cycles on Impartial Solitaire Clobber.
Electronic Notes in Discrete Mathematics 01/2011; 37:177182. DOI: 10.1016/j.endm.2011.05.031
Source: DBLP
 Citations (5)
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Article: An introduction to Clobber
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ABSTRACT: Clobber is an allsmall game usually played on a checkerboard but the rules easily generalize to play on an arbitrary graph. We show that, on a graph, determining the value of the game is NPhard. We also examine clobber on a 1 × n and a 2 × n strip.Integers 08/2005; 5(2).  [Show abstract] [Hide abstract]
ABSTRACT: The oneplayer game Solitaire Clobber was introduced by Demaine et al. Beaudou et al. considered a variation called SC2. Black and white stones are located on the vertices of a given graph. A move consists in picking a stone to replace an adjacent stone of the opposite color. The objective is to minimize the number of remaining stones. The game is interesting if there is at least one stone of each color. In this paper, we investigate the case of Hamming graphs. We prove that game configurations on such graphs can always be reduced to a single stone, except for hypercubes. Nevertheless, hypercubes can be reduced to two stones.01/2008;  [Show abstract] [Hide abstract]
ABSTRACT: We prove that the oneplayer game Solitaire Clobber 2 is equivalent to an optimization problem on a set of words defined by seven classes of forbidden patterns when played on the line or on the cycle. This enables us to show that this game is solvable in linear time. Using this word representation, we also prove that, playing on the cycle, it is always possible to remove at least 2n/3 pawns, and we give a configuration for which it is not possible to do better, answering questions recently raised by Duchêne et al.INTEGERS: ELECTRONIC JOURNAL OF COMBINATORIAL NUMBER THEORY. 01/2008; 8.
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