Game coloring the Cartesian product of graphs
نویسندگان
چکیده
منابع مشابه
Game coloring the Cartesian product of graphs
This article proves the following result: Let G and G′ be graphs of orders n and n′, respectively. Let G∗ be obtained from G by adding to each vertex a set of n′ degree 1 neighbors. If G∗ has game coloring number m and G′ has acyclic chromatic number k, then the Cartesian product G G′ has game chromatic number at most k(k+m − 1). As a consequence, the Cartesian product of two forests has game c...
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The game chromatic number χg is considered for the Cartesian product G 2 H of two graphs G and H. We determine exact values of χg(G2H) when G and H belong to certain classes of graphs, and show that, in general, the game chromatic number χg(G2H) is not bounded from above by a function of game chromatic numbers of graphs G and H. An analogous result is proved for the game coloring number colg(G2...
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let $g$ be a graph and $chi^{prime}_{aa}(g)$ denotes the minimum number of colors required for an acyclic edge coloring of $g$ in which no two adjacent vertices are incident to edges colored with the same set of colors. we prove a general bound for $chi^{prime}_{aa}(gsquare h)$ for any two graphs $g$ and $h$. we also determine exact value of this parameter for the cartesian product of ...
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ژورنال
عنوان ژورنال: Journal of Graph Theory
سال: 2008
ISSN: 0364-9024,1097-0118
DOI: 10.1002/jgt.20338