Game Chromatic Number of Some Regular Graphs
نویسندگان
چکیده
منابع مشابه
Game chromatic number of graphs
y Abstract We show that if a graph has acyclic chromatic number k, then its game chromatic number is at most k(k + 1). By applying the known upper bounds for the acyclic chromatic numbers of various classes of graphs, we obtain upper bounds for the game chromatic number of these classes of graphs. In particular, since a planar graph has acyclic chromatic number at most 5, we conclude that the g...
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Given any integer d ≥ 3, let k be the smallest integer such that d < 2k log k. We prove that with high probability the chromatic number of a random d-regular graph is k, k + 1, or k + 2.
متن کاملCircular game chromatic number of graphs
In a circular r-colouring game on G, Alice and Bob take turns colour the vertices of G with colours from the circle S(r) of perimeter r. Colours assigned to adjacent vertices need to have distance at least 1 in S(r). Alice wins the game if all vertices are coloured, and Bob wins the game if some uncoloured vertices have no legal colour. The circular game chromatic number χcg(G) of G is the infi...
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Suppose G = (V, E) is a graph. The game chromatic number of G is defined through a two-person game: the colouring game. Given a graph G and a set C of colours, Alice and Bob, with Alice playing first, take turns in playing the game. Each play by either player consists of colouring an uncoloured vertex of G with a colour from C. Both players need to respect the rule that no adjacent vertices sho...
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Given a graph G and an integer k, two players take turns coloring the vertices of G one by one using k colors so that neighboring vertices get different colors. The first player wins iff at the end of the game all the vertices of G are colored. The game chromatic number χg(G) is the minimum k for which the first player has a winning strategy. In this paper we analyze the asymptotic behavior of ...
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ژورنال
عنوان ژورنال: Open Journal of Discrete Mathematics
سال: 2019
ISSN: 2161-7635,2161-7643
DOI: 10.4236/ojdm.2019.94012