#### Title

Distance Coloring

#### Abstract

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 TeX and NP-hard for TeX .

#### Repository Citation

Sharp, A. 2007. "Distance Coloring," in Proceedings of the 15th Annual European Symposium on Algorithms, 2007. Lecture Notes In Computer Science.

#### Publisher

Springer

#### Publication Date

1-1-2007

#### Publication Title

Lecture Notes In Computer Science

#### Department

Computer Science

#### Document Type

Conference Proceeding

#### DOI

10.1007/978-3-540-75520-3_46

#### Language

English

#### Format

text