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arXiv · 1204.1989

Multiple Petersen subdivisions in permutation graphs

Tomáš Kaiser·Jean-Sébastien Sereni·Zelealem Yilma
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Abstract

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.

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Tomáš Kaiser, Jean-Sébastien Sereni, Zelealem Yilma. 2012-04-09. Multiple Petersen subdivisions in permutation graphs. https://arxiv.org/abs/1204.1989

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