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The maximum k-colorable subgraph problem for chordal graphs. (English) Zbl 0653.68070
Summary: We discuss the problems of finding maximum and connected maximum k- colorable subgraphs in chordal graphs. We prove that the problems are polynomially solvable when k is fixed and NP-hard when k is not fixed. As a special case, we can find in polynomial time the maximum induced tree and forest of a chordal graph.

MSC:
68R10 Graph theory (including graph drawing) in computer science
68Q25 Analysis of algorithms and problem complexity
05C15 Coloring of graphs and hypergraphs
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