Chromatic Number for a Generalization of Cartesian Product Graphs
نویسندگان
چکیده
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 bound is best possible by proving that f(G; d) = kd when G is the class of all k-colorable graphs. We also show that f(G; d) ≥ ⌊√
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عنوان ژورنال:
- Electr. J. Comb.
دوره 16 شماره
صفحات -
تاریخ انتشار 2009