Locally bounded k-colorings of trees
RAIRO - Operations Research - Recherche Opérationnelle, Volume 43 (2009) no. 1, pp. 27-33.

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 logn) time. We also show that our algorithm can be adapted to the case of k-colorings for fixed k.

DOI: 10.1051/ro/2009003
Classification: 05C15, 90C39
Keywords: bounded graph coloring, tree, dynamic programming
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     author = {Bentz, C. and Picouleau, C.},
     title = {Locally bounded $k$-colorings of trees},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {27--33},
     publisher = {EDP-Sciences},
     volume = {43},
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     zbl = {1158.05317},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ro/2009003/}
}
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Bentz, C.; Picouleau, C. Locally bounded $k$-colorings of trees. RAIRO - Operations Research - Recherche Opérationnelle, Volume 43 (2009) no. 1, pp. 27-33. doi : 10.1051/ro/2009003. http://archive.numdam.org/articles/10.1051/ro/2009003/

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