Displaying similar documents to “Colouring game and generalized colouring game on graphs with cut-vertices”

How Long Can One Bluff in the Domination Game?

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....

Note On The Game Colouring Number Of Powers Of Graphs

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.

R ( 3 , 4 ) = 17 .

Pralat, Pawel (2008)

The Electronic Journal of Combinatorics [electronic only]

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Domination Game Critical Graphs

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...

Game list colouring of graphs.

Borowiecki, M., Sidorowicz, E., Tuza, Zs. (2007)

The Electronic Journal of Combinatorics [electronic only]

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