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doi:10.1016/S0012-365X(98)00169-1 
Copyright © 1999 Published by Elsevier Science B.V.
On the complexity of a restricted list-coloring problem
Received 11 June 1997;
revised 16 March 1998;
accepted 13 April 1998. ;
Available online 3 March 1999.
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Abstract
We investigate a restricted list-coloring problem. Given a graph G = (V, E), a non empty set of colors L, and a nonempty subset L(v) of L for each vertex v, find an L-coloring of G with the size of each class of colors being equal to a given integer. This restricted list-coloring problem was proposed by de Werra. We prove that this problem is N P-Complete even if the graph is a path with at most two colors on each vertex list. We then give a polynomial algorithm which solves this problem for the case where the total number of colors occurring in all lists is fixed.
