Nonrepetitive Colorings of GraphsA Survey

Grytczuk, Jaroslaw

doi:https://doi.org/10.1155/2007/74639

International Journal of Mathematics and Mathematical Sciences

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Review Article | Open Access

Volume 2007 | Article ID 074639 | https://doi.org/10.1155/2007/74639

Nonrepetitive Colorings of GraphsA Survey

Jaroslaw Grytczuk^1,2

Academic Editor: George E. Andrews

Received08 Aug 2006

Revised04 Nov 2006

Accepted29 Nov 2006

Published14 Jan 2007

Abstract

A vertex coloring f of a graph G is nonrepetitive if there are no integer r≥1 and a simple path v1,…,v2r in G such that f(vi)=f(vr+i) for all i=1,…,r. This notion is a graph-theoretic variant of nonrepetitive sequences of Thue. The paper surveys problems and results on this topic.

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Copyright

Copyright © 2007 Jarosław Grytczuk. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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