Distance Coloring
نویسنده
چکیده
Given a graphG = (V,E), a (d, k)-coloring is a function from the vertices V to colors {1, 2, . . . , k} such that any two vertices within distance d of each other are assigned different colors. We determine the complexity of the (d, k)-coloring problem for all d and k, and enumerate some interesting properties of (d, k)-colorable graphs. Our main result is the discovery of a dichotomy between polynomial and NP-hard instances: for fixed d ≥ 2, the distance coloring problem is polynomial time for k ≤ b 3d 2 c and NP-hard for k > b 3d 2 c.
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تاریخ انتشار 2007