Relaxed very asymmetric coloring games
نویسندگان
چکیده
منابع مشابه
Asymmetric graph coloring games
We introduce the (a; b)-coloring game, an asymmetric version of the coloring game played by two players Alice and Bob on a finite graph, which differs from the standard version in that, in each turn, Alice colors a vertices and Bob colors b vertices. We also introduce a related game, the (a; b)-marking game. We analyze these games and determine the (a; b)chromatic numbers and (a;b)-coloring num...
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This note generalizes the (a, b)-coloring game and the (a, b)-marking game which were introduced by Kierstead [7] for undirected graphs to directed graphs. We prove that the (a, b)-chromatic and (a, b)-coloring number for the class of orientations of forests is b + 2 if b ≤ a, and infinity otherwise. From these results we deduce upper bounds for the (a, b)-coloring number of oriented outerplana...
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Consider the following game on a graph G: Alice and Bob take turns coloring the vertices of G properly from a fixed set of colors; Alice wins when the entire graph has been colored, while Bob wins when some uncolored vertices have been left. The game chromatic number of G is the minimum number of colors that allows Alice to win the game. The game Grundy number of G is defined similarly except t...
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In this paper we investigate a variation of the graph coloring game, as studied in [2]. In the original coloring game, two players, Alice and Bob, alternate coloring vertices on a graph with legal colors from a fixed color set, where a color α is legal for a vertex if said vertex has no neighbors colored α. Other variations of the game change this definition of a legal color. For a fixed color ...
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Let P be a hereditary family of graphs. A relaxed coloring of a graph G = (V; E) with respect to P is an assignment of colors to ver-tices of G so that each color class induces a graph which is the disjoint union of members of P. The P-chromatic number P (G) of G is the minimum number of colors in a relaxed coloring of G with respect to P. We study the relation between the girth and the P-chrom...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2009
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.11.058