Geodesic
The Black-and-White Coloring Problem on Trees
Journal of Graph Algorithms and Applications, Tome 13 (2009) no. 2, pp. 133-152.

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Given a graph G and positive integers b and w, the black-and-white coloring problem asks about the existence of a partial vertex-coloring of G, with b vertices colored black and w white, such that there is no edge between a black and a white vertex. We suggest an improved algorithm for solving this problem on trees. 
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     title = {The {Black-and-White} {Coloring} {Problem} on {Trees}},
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Daniel Berend; Shira Zucker. The Black-and-White Coloring Problem on Trees. Journal of Graph Algorithms and Applications, Tome 13 (2009) no. 2, pp. 133-152. doi : 10.7155/jgaa.00180. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00180/

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