Precoloring Extension with Fixed Color Bound
نویسنده
چکیده
Precoloring Extension (shortly PrExt) is the following problem: Given a graph G with some precolored vertices and a color bound k, can the precoloring of G be extended to a proper coloring of all vertices of G using not more than k colors? Answering an open problem from [6], we prove that PrExt with fixed color bound k = 3 is NP-complete for bipartite (and even planar) graphs, and we prove a general result on parametrized PrExt. We also give a simplified argument why PrExt with fixed color bound is solvable in polynomial time for graphs of bounded treewidth (and hence also for chordal graphs).
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