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Forbidden minors characterization of partial 3-trees. (English) Zbl 0701.05016
A partial k-tree is a subgraph of a graph that can be reduced to the complete graph of order k by a sequence of operations each being a removal of a degree k vertex with completely connected neighbours. In the paper the class of partial 3-trees is characterized by its set of four minimal forbidden minors.
Reviewer: P.Kirschenhofer

MSC:
05C05 Trees
Keywords:
graph minors; trees
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[1] Arnborg, S., Reduced state enumeration—another algorithm for reliability evaluation, IEEE trans. reliability, R-27, 101-105, (1978) · Zbl 0436.60062
[2] Arnborg, S., Efficient algorithms for combinatorial problems on graphs with bounded decomposability—a survey, Bit, 25, 2-33, (1985) · Zbl 0573.68018
[3] Arnborg, S.; Corneil, D.G.; Proskurowski, A., Complexity of finding embeddings in a k-tree, SIAM J. alg. and discr. methods, 8, 277-284, (1987) · Zbl 0611.05022
[4] Arnborg, S.; Proskurowski, A., Characterization and recognition of partial 3-trees, SIAM J. alg. and discr. methods, 7, 305-314, (1986) · Zbl 0597.05027
[5] Arnborg, S.; Proskurowski, A., Linear time algorithms for NP-hard problems on graphs embedded in k-trees, (), (to appear in Discr. Appl. Math., 1989)
[6] Colbourn, C.J.; Proskurowski, A., Concurrent transmissions in broadcast networks, (), 128-136, LNCS · Zbl 0554.94021
[7] Farley, A.M., Networks, immune to isolated failures, Networks, 11, 255-268, (1981) · Zbl 0459.94036
[8] Farley, A.M.; Proskurowski, A., Networks immune to isolated line failures, Networks, 12, 393-403, (1982) · Zbl 0493.94020
[9] Neufeld, E.M.; Colbourn, C.J., The most reliable series-parallel networks, TR 83-7, (1983), Dept. of Computing Science, University of Saskatchewan
[10] Proskurowski, A., Separating subgraphs in k-trees: cables and caterpillars, Discr. math., 49, 275-285, (1984) · Zbl 0543.05041
[11] Robertson, N.; Seymour, P.D., Disjoint paths—a survey, SIAM J. alg. discr. meth., 6, 300-305, (1985) · Zbl 0565.05045
[12] Wald, A.; Colbourn, C.J., Steiner trees, partial 2-trees, and minimum IFI networks, Networks, 13, 159-167, (1983) · Zbl 0529.68036
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