The S-packing chromatic number of a graph
نویسندگان
چکیده
Let S = (a1, a2, . . .) be an infinite nondecreasing sequence of positive integers. An S-packing k-coloring of a graph G is a mapping from V (G) to {1, 2, . . . , k} such that vertices with color i have pairwise distance greater than ai, and the S-packing chromatic number χS(G) of G is the smallest integer k such that G has an S-packing k-coloring. This concept generalizes the concept of proper coloring (when S = (1, 1, 1, . . .)) and broadcast coloring (when S = (1, 2, 3, 4, . . .)). In this paper, we consider bounds on the parameter and its relationship with other parameters. We characterize the graphs with χS = 2 and determine χS for several common families of graphs. We examine χS for the infinite path and give some exact values and asymptotic bounds. Finally we consider complexity questions, especially about recognizing graphs with χS = 3.
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عنوان ژورنال:
- Discussiones Mathematicae Graph Theory
دوره 32 شماره
صفحات -
تاریخ انتشار 2012