Abstract
In the precoloring extension problem (PrExt) we are given a graph with some of the vertices having preassigned colors and it has to be decided whether this coloring can be extended to a proper κ-coloring of the whole graph. 1-PrExt is the special case where every color is assigned to at most one vertex in the precoloring. Answering an open question of Hujter and Tuza [7], we show that the 1-PrExt problem can be solved in polynomial time for chordal graphs.
Research is supported in part by grants OTKA 44733, 42559 and 42706 of the Hungarian National Science Fund.
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Marx, D. (2006). Precoloring Extension on Chordal Graphs. In: Bondy, A., Fonlupt, J., Fouquet, JL., Fournier, JC., Ramírez Alfonsín, J.L. (eds) Graph Theory in Paris. Trends in Mathematics. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-7400-6_20
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