Distance Coloring

Given a graph G = (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 ≤ 3d 2 and NP-hard for k > 3d 2 . Key words: graph coloring, power graphs, complexity threshold

• Type: Conference
• Year: 2007
• Where: ESA
• Authors: Alexa Sharp
• Keywords: Distance Coloring Problem, Different Colors, ESA 2007, NP-hard Instances