Game chromatic number of Cartesian product graphs.
Bartnicki, T., Bresar, B., Grytczuk, J., Kovse, M., Miechowicz, Z., Peterin, I. (2008)
The Electronic Journal of Combinatorics [electronic only]
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Bartnicki, T., Bresar, B., Grytczuk, J., Kovse, M., Miechowicz, Z., Peterin, I. (2008)
The Electronic Journal of Combinatorics [electronic only]
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Kárná, Lucie
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This article formalizes some aspects of the board game Carcassonne. Combinatorical problems related to the number of tile types are mentioned. Then the paper describes a game map using graph theory.
S. Nakamura, D. Minematsu, T. Kitagawa, Y. Naito, R. Fujii, T. hieda, R. Miyadera (2012)
Visual Mathematics
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Nancy E. Clarke, Richard J. Nowakowski (2005)
Discussiones Mathematicae Graph Theory
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In this version of the Cops and Robber game, the cops move in tandems, or pairs, such that they are at distance at most one from each other after every move. The problem is to determine, for a given graph G, the minimum number of tandems sufficient to guarantee a win for the cops. We investigate this game on three graph products, the Cartesian, categorical and strong products.
W. Rytter (1987)
Applicationes Mathematicae
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Yang, Daqing, Zhu, Xuding (2010)
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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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.
Nowakowski, Richard J., Ottaway, Paul (2005)
Integers
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Cincotti, Alessandro (2009)
Integers
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Nešetřil, J., Sopena, E. (2001)
The Electronic Journal of Combinatorics [electronic only]
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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....
Kelly, Annela R. (2006)
International Journal of Mathematics and Mathematical Sciences
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Mukkamala, Padmini, Pálvölgyi, Dömötör (2010)
The Electronic Journal of Combinatorics [electronic only]
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