Game chromatic number of lexicographic product 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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ژورنال
عنوان ژورنال: AKCE International Journal of Graphs and Combinatorics
سال: 2015
ISSN: 0972-8600,2543-3474
DOI: 10.1016/j.akcej.2015.11.017