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New results about impartial solitaire clobber

Eric Duchêne, Sylvain Gravier, Julien Moncel (2009)

RAIRO - Operations Research

Impartial Solitaire Clobber is a one-player version of the combinatorial game Clobber, introduced by Albert et al. in 2002. The initial configuration of Impartial Solitaire Clobber is a graph, such that there is a stone placed on each of its vertex, each stone being black or white. A move of the game consists in picking a stone, and clobbering an adjacent stone of the opposite color. By clobbering we mean that the clobbered stone is removed from the graph, and replaced by the clobbering one....

Note On The Game Colouring Number Of Powers Of Graphs

Stephan Dominique Andres, Andrea Theuser (2016)

Discussiones Mathematicae Graph Theory

We generalize the methods of Esperet and Zhu [6] providing an upper bound for the game colouring number of squares of graphs to obtain upper bounds for the game colouring number of m-th powers of graphs, m ≥ 3, which rely on the maximum degree and the game colouring number of the underlying graph. Furthermore, we improve these bounds in case the underlying graph is a forest.

Note: The Smallest Nonevasive Graph Property

Michał Adamaszek (2014)

Discussiones Mathematicae Graph Theory

A property of n-vertex graphs is called evasive if every algorithm testing this property by asking questions of the form “is there an edge between vertices u and v” requires, in the worst case, to ask about all pairs of vertices. Most “natural” graph properties are either evasive or conjectured to be such, and of the few examples of nontrivial nonevasive properties scattered in the literature the smallest one has n = 6. We exhibit a nontrivial, nonevasive property of 5-vertex graphs and show that...

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