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.
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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W. Rytter (1987)
Applicationes Mathematicae
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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.
Bartnicki, T., Bresar, B., Grytczuk, J., Kovse, M., Miechowicz, Z., Peterin, I. (2008)
The Electronic Journal of Combinatorics [electronic only]
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Pralat, Pawel (2008)
The Electronic Journal of Combinatorics [electronic only]
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Yang, Daqing, Zhu, Xuding (2010)
The Electronic Journal of Combinatorics [electronic only]
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Csilla Bujtás, Sandi Klavžar, Gašper Košmrlj (2015)
Discussiones Mathematicae Graph Theory
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The domination game is played on a graph G by two players who alternately take turns by choosing a vertex such that in each turn at least one previously undominated vertex is dominated. The game is over when each vertex becomes dominated. One of the players, namely Dominator, wants to finish the game as soon as possible, while the other one wants to delay the end. The number of turns when Dominator starts the game on G and both players play optimally is the graph invariant γg(G), named...
S. F. Kapoor, Linda M. Lesniak (1976)
Colloquium Mathematicae
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Zlatomir Lukić (1982)
Publications de l'Institut Mathématique
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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.
Jaroslav Ivančo (2016)
Discussiones Mathematicae Graph Theory
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A graph G is called supermagic if it admits a labelling of the edges by pairwise di erent consecutive integers such that the sum of the labels of the edges incident with a vertex is independent of the particular vertex. In this paper we will introduce some constructions of supermagic labellings of some graphs generalizing double graphs. Inter alia we show that the double graphs of regular Hamiltonian graphs and some circulant graphs are supermagic.