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  • A permutation graph is a cubic graph admitting a 1-factor M whose complement consists of two chordless cycles. Extending results of Ellingham and of Goldwasser and Zhang, we prove that if e is an edge of M such that every 4-cycle containing an edge of M contains e, then e is contained in a subdivision of the Petersen graph of a special type. In particular, if the graph is cyclically 5-edge-connected, then every edge of M is contained in such a subdivision. Our proof is based on a characterization of cographs in terms of twin vertices. We infer a linear lower bound on the number of Petersen subdivisions in a permutation graph with no 4-cycles, and give a construction showing that this lower bound is tight up to a constant factor.
  • A permutation graph is a cubic graph admitting a 1-factor M whose complement consists of two chordless cycles. Extending results of Ellingham and of Goldwasser and Zhang, we prove that if e is an edge of M such that every 4-cycle containing an edge of M contains e, then e is contained in a subdivision of the Petersen graph of a special type. In particular, if the graph is cyclically 5-edge-connected, then every edge of M is contained in such a subdivision. Our proof is based on a characterization of cographs in terms of twin vertices. We infer a linear lower bound on the number of Petersen subdivisions in a permutation graph with no 4-cycles, and give a construction showing that this lower bound is tight up to a constant factor. (en)
Title
  • Multiple Petersen subdivisions in permutation graphs
  • Multiple Petersen subdivisions in permutation graphs (en)
skos:prefLabel
  • Multiple Petersen subdivisions in permutation graphs
  • Multiple Petersen subdivisions in permutation graphs (en)
skos:notation
  • RIV/49777513:23520/13:43918088!RIV14-MSM-23520___
http://linked.open...avai/riv/aktivita
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  • I, P(GBP202/12/G061)
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  • 1
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  • 90146
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  • RIV/49777513:23520/13:43918088
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  • cograph; Petersen subdivision; permutation graph; graph theory (en)
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  • US - Spojené státy americké
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  • [63657F1331B8]
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  • ELECTRONIC JOURNAL OF COMBINATORICS
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  • 20
http://linked.open...iv/tvurceVysledku
  • Kaiser, Tomáš
  • Sereni, Jean-Sébastien
  • Yilma, Zelealem B.
issn
  • 1077-8926
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  • 23520
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