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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Nowakowski, Richard J., Ottaway, Paul (2005)
Integers
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Yang, Daqing, Zhu, Xuding (2010)
The Electronic Journal of Combinatorics [electronic only]
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S. Nakamura, D. Minematsu, T. Kitagawa, Y. Naito, R. Fujii, T. hieda, R. Miyadera (2012)
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.
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.
Borowiecki, M., Sidorowicz, E., Tuza, Zs. (2007)
The Electronic Journal of Combinatorics [electronic only]
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Lee, Jae-Ha, Park, Chong-Dae, Chwa, Kyung-Yong (2001)
Journal of Graph Algorithms and Applications
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Julien Bernet, David Janin, Igor Walukiewicz (2002)
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications
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It is proposed to compare strategies in a parity game by comparing the sets of behaviours they allow. For such a game, there may be no winning strategy that encompasses all the behaviours of all winning strategies. It is shown, however, that there always exists a permissive strategy that encompasses all the behaviours of all memoryless strategies. An algorithm for finding such a permissive strategy is presented. Its complexity matches currently known upper bounds for the simpler problem...
Fraenkel, Aviezri S. (1996)
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.