Remarks on pebble games on graphs
W. Rytter (1987)
Applicationes Mathematicae
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W. Rytter (1987)
Applicationes Mathematicae
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Elżbieta Sidorowicz (2010)
Discussiones Mathematicae Graph Theory
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For k ≥ 2 we define a class of graphs 𝓗 ₖ = {G: every block of G has at most k vertices}. The class 𝓗 ₖ contains among other graphs forests, Husimi trees, line graphs of forests, cactus graphs. We consider the colouring game and the generalized colouring game on graphs from 𝓗 ₖ.
Boštan Brešar, Paul Dorbec, Sandi Klavžar, Gašpar Košmrlj (2017)
Discussiones Mathematicae Graph Theory
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The domination game is played on an arbitrary graph G by two players, Dominator and Staller. The game is called Game 1 when Dominator starts it, and Game 2 otherwise. In this paper bluff graphs are introduced as the graphs in which every vertex is an optimal start vertex in Game 1 as well as in Game 2. It is proved that every minus graph (a graph in which Game 2 finishes faster than Game 1) is a bluff graph. A non-trivial infinite family of minus (and hence bluff) graphs is established....
Masakazu Naito, Toshiyuki Yamauchi, Hiroshi Matsui, Taishi Inoue, Yuuki Tomari, Koichiro Nishimura, Takuma Nakaoka, Daisuke Minematsu, Ryohei Miyadera (2009)
Visual Mathematics
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Stephan Dominique Andres, Andrea Theuser (2016)
Discussiones Mathematicae Graph Theory
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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.
Bartnicki, T., Bresar, B., Grytczuk, J., Kovse, M., Miechowicz, Z., Peterin, I. (2008)
The Electronic Journal of Combinatorics [electronic only]
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Fraenkel, Aviezri S. (1996)
The Electronic Journal of Combinatorics [electronic only]
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B. Florkiewicz (1969)
Applicationes Mathematicae
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Andrzej Młodak (2007)
Applicationes Mathematicae
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We prove new axiomatizations of the Shapley value and the Banzhaf value, defined on the class of nonnegative constant-sum games with nonzero worth of the grand coalition as well as on nonnegative bilateral games with nonzero worth of the grand coalition. A characteristic feature of the latter class of cooperative games is that for such a game any coalition and its complement in the set of all players have the same worth. The axiomatizations are then generalized to the entire class of...
Mesdal, G.A., Ottaway, P. (2007)
Integers
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Kelly, Annela R. (2006)
International Journal of Mathematics and Mathematical Sciences
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Hans Keiding (2006)
Banach Center Publications
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The aspiration core of a TU game was introduced by Bennett [1] as a payoff vector which is undominated and achievable in the sense that each player belongs to a coalition which can obtain the specified payoff for its members, and which minimizes the distance to the set of aggregate feasible payoffs among all such payoff vectors. In the paper a set of axioms is proposed which characterize the aspiration core, which may be considered as an extension of the core to a much larger set of...