Multiple Petersen subdivisions in permutation graphs
Combinatorics
2012-04-11 v1
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.
Keywords
Cite
@article{arxiv.1204.1989,
title = {Multiple Petersen subdivisions in permutation graphs},
author = {Tomáš Kaiser and Jean-Sébastien Sereni and Zelealem Yilma},
journal= {arXiv preprint arXiv:1204.1989},
year = {2012}
}