Interval vertex-coloring of a graph with forbidden colors

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Abstract

We consider a problem of interval coloring the vertices of a graph under the stipulation that certain colors cannot be used for some vertices. We give lower and upper bounds on the minimum number of colors required for such a coloring. Since the general problem is NP-complete, we investigate its complexity in some special cases with a particular reference to those that can be solved by a polynomial-time algorithm.

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