Locally bounded k-colorings of trees

Issue		RAIRO Oper. Res. Volume 43, Number 1, January-March 2009


Page(s)		27 - 33
DOI		10.1051/ro/2009003
Published online		28 January 2009

RAIRO-Oper. Res. 43 (2009) 27-33
DOI: 10.1051/ro/2009003

Locally bounded k-colorings of trees

C. Bentz¹ and C. Picouleau²

¹ CEDRIC, CNAM, Paris, France; cedric.bentz@cnam.fr
² CEDRIC, CNAM, Paris, France; chp@cnam.fr

Received June 19, 2007. Accepted July 28, 2008 Published online 28 January 2009

Abstract
Given a tree T with n vertices, we show, by using a dynamic programming approach, that the problem of finding a 3-coloring of T respecting local (i.e., associated with p prespecified subsets of vertices) color bounds can be solved in $O(n^{6p-1} \log n)$ time. We also show that our algorithm can be adapted to the case of k-colorings for fixed k.

Mathematics Subject Classification. 05C15, 90C39.

Key words: Bounded graph coloring, tree, dynamic programming.

© EDP Sciences, ROADEF, SMAI 2009

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