The complexity of nonrepetitive coloring

Authors:
Dániel Marx;Marcus Schaefer
Affiliations:
Department of Computer Science and Information Theory, Budapest University of Technology and Econonomics, Budapest H-1521, Hungary;Department of Computer Science, DePaul University, Chicago, IL 60604, United States
Venue:
Discrete Applied Mathematics
Year:
2009

Citing 5
Cited 2

Color-coding

Journal of the ACM (JACM)
Nonrepetitive colorings of graphs

Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
Pattern avoidance: themes and variations

Theoretical Computer Science - Combinatorics on words
Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)

Applied Combinatorics on Words (Encyclopedia of Mathematics and its Applications)
Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)

Parameterized Complexity Theory (Texts in Theoretical Computer Science. An EATCS Series)

New Constructive Aspects of the Lovász Local Lemma

Journal of the ACM (JACM)
Characterisations and examples of graph classes with bounded expansion

European Journal of Combinatorics

Quantified Score

Hi-index	0.04

Visualization

Abstract

A coloring of a graph is nonrepetitive if the graph contains no path that has a color pattern of the form xx (where x is a sequence of colors). We show that determining whether a particular coloring of a graph is nonrepetitive is coNP-hard, even if the number of colors is limited to four. The problem becomes fixed-parameter tractable, if we only exclude colorings xx up to a fixed length k of x.