Weak acyclic coloring and 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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A vertex coloring of a graph G is called acyclic if no two adjacent vertices have the same color and there is no two-colored cycle in G. The acyclic chromatic number of G , denoted by A ( G ) , is the least number of colors in an acyclic coloring of G. We show that if G has maximum degree d, then A ( G ) = O(d413) as d+m. This settles a problem of Erdos who conjectured, in 1976, that A ( G ) = ...
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Coloring is an abstraction for partitioning a set of objects into a few independent sets. The notion of independence and the associated coloring rules vary from context to context. In the simplest case, adjacent vertices in a graph are required to receive different colors ( proper coloring). In parallel scientific computing, a proper coloring is used to identify computational subtasks that can ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2006
ISSN: 0012-365X
DOI: 10.1016/j.disc.2004.07.042