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Locally bounded k -colorings of trees

Cédric Bentz 1 Christophe Picouleau 1
1 CEDRIC - OC - CEDRIC. Optimisation Combinatoire
CEDRIC - Centre d'études et de recherche en informatique et communications
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.
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Cédric Bentz, Christophe Picouleau. Locally bounded k -colorings of trees. RAIRO - Operations Research, EDP Sciences, 2009, 43 (1), pp.27-33. ⟨10.1051/ro/2009003⟩. ⟨hal-02436823⟩

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