Algorithms for Square Roots of Graphs
SIAM Journal on Discrete Mathematics
An algorithm for the Tutte polynomials of graphs of bounded treewidth
Discrete Mathematics
Coloring powers of planar graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
Partitioning graphs into generalized dominating sets
Nordic Journal of Computing
Channel Assignment on Strongly-Simplicial Graphs
IPDPS '03 Proceedings of the 17th International Symposium on Parallel and Distributed Processing
Evaluating the Tutte Polynomial for Graphs of Bounded Tree-Width
Combinatorics, Probability and Computing
Graph Theory With Applications
Graph Theory With Applications
Logic and Program Semantics
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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⌋.