Yannakakis, Mihalis; Gavril, Fanica The maximum k-colorable subgraph problem for chordal graphs. (English) Zbl 0653.68070 Inf. Process. Lett. 24, 133-137 (1987). 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. Cited in 3 ReviewsCited in 59 Documents MSC: 68R10 Graph theory (including graph drawing) in computer science 68Q25 Analysis of algorithms and problem complexity 05C15 Coloring of graphs and hypergraphs Keywords:NP-complete; k-colorable; chordal graphs PDF BibTeX XML Cite \textit{M. Yannakakis} and \textit{F. Gavril}, Inf. Process. Lett. 24, 133--137 (1987; Zbl 0653.68070) Full Text: DOI References: [1] Booth, K. S.; Lueker, G. S., Testing for the consecutive ones property, interval graphs, and graph planarity using PQ-tree algorithms, J. Comput. System Sci., 13, 335-379 (1976) · Zbl 0367.68034 [2] Frank, A., On chain and antichain families of a partially ordered set, J. Combin. Theory Ser. B, 29, 176-184 (1980) · Zbl 0443.06003 [3] Garey, M. R.; Johnson, D. S., Computer and Intractability: A Guide to the Theory of NP-Completeness (1978), Freeman: Freeman San Francisco, CA · Zbl 0379.68035 [4] Gavril, F., The intersection graphs of subtrees in trees are exactly the chordal graphs, J. Combin. Theory Ser. B, 16, 47-56 (1974) · Zbl 0266.05101 [5] Golumbic, M. C., Algorithmic Graph Theory and Perfect Graphs (1980), Academic Press: Academic Press New York · Zbl 0541.05054 [6] Greene, C., Some partitions associated with a partially ordered set, J. Combin. Theory Ser. A, 20, 69-79 (1976) · Zbl 0323.06002 [7] Greene, C.; Kleitman, D., The structure of Sperner \(k\)-families, J. Combin. Theory Ser. A, 20, 41-68 (1976) · Zbl 0361.05016 [8] Grötschel, M.; Lovasz, L.; Schrijver, A., The ellipsoid method and its consequences in combinatorial optimization, Combinatorica, 1, 169-197 (1981) · Zbl 0492.90056 [9] Lovasz, L., Perfect graphs, (Beineke, L. W.; Wilson, R. J., Selected Topics in Graph Theory, Vol. 2 (1983), Academic Press: Academic Press New York), 55-87 [10] Rose, D. J.; Tarjan, R. E.; Lueker, G. S., Algorithmic aspects of vertex elimination on graphs, SIAM J. Comput., 5, 266-283 (1976) · Zbl 0353.65019 [11] Yannakakis, M., Node-deletion problems on bipartite graphs, SIAM J. Comput., 10, 310-327 (1981) · Zbl 0468.05044 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.