Chromatic number of Cartesian sum of two graphs
نویسندگان
چکیده
منابع مشابه
Game Chromatic Number of Cartesian Product Graphs
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[H] be the lexicographic product of graphs G and H and let G⊕H be their Cartesian sum. It is proved that if G is a nonbipartite graph, then for any graph H, χ(G[H]) ≥ 2χ(H)+d k e, where 2k+1 is the length of a shortest odd cycle of G. Chromatic numbers of the Cartesian sum of graphs are also considered. It is shown in particular that for χ–critical and not complete graphs G and H, χ(G ⊕ H)...
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The distinguishing chromatic number χD (G) of a graph G is the least integer k such that there is a proper k-coloring of G which is not preserved by any nontrivial automorphism of G. We study the distinguishing chromatic number of Cartesian products of graphs by focusing on how much it can exceed the trivial lower bound of the chromatic number χ(·). Our main result is that for every graph G, th...
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Let G be a class of graphs. A d-fold grid over G is a graph obtained from a d-dimensional rectangular grid of vertices by placing a graph from G on each of the lines parallel to one of the axes. Thus each vertex belongs to d of these subgraphs. The class of d-fold grids over G is denoted by Gd. Let f(G; d) = maxG∈Gd χ(G). If each graph in G is k-colorable, then f(G; d) ≤ kd. We show that this b...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1968
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1968-0223273-9