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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.doi:10.1051/ro/2009003 fatcat:qli3whnszjfdtnahwl3jpthzym