"http://www.combinatorics.org/ojs/index.php/eljc/article/view/v20i1p37/pdf" . "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." . . "Kaiser, Tom\u00E1\u0161" . . . "ELECTRONIC JOURNAL OF COMBINATORICS" . "RIV/49777513:23520/13:43918088" . "cograph; Petersen subdivision; permutation graph; graph theory"@en . . "1"^^ . . "3"^^ . . . . "Multiple Petersen subdivisions in permutation graphs"@en . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . . "9"^^ . "Multiple Petersen subdivisions in permutation graphs"@en . "1077-8926" . "Multiple Petersen subdivisions in permutation graphs" . . . . "23520" . "Sereni, Jean-S\u00E9bastien" . . "[63657F1331B8]" . . "20" . . "I, P(GBP202/12/G061)" . "RIV/49777513:23520/13:43918088!RIV14-MSM-23520___" . "Yilma, Zelealem B." . "90146" . . "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 . "Multiple Petersen subdivisions in permutation graphs" . . . "1" .