Local complementation and interlacement graphs

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Abstract

Let M be a binary matroid on a set E. We show that by performing a sequence of local complementations at ei (i=1,...,n) on the principal interlacement graph of M, for any ordering of E = {e1,...,en}, we obtain a bipartite graph whose two sets of vertices define a partition of E into a base B and a cobase B⊥ of the matroid M. We then give a characterisation of bipartite chordable graphs and, as an application, we give a short proof of Pierre Rosenstiehl's characterization of planar graphs: a graph with a trivial bicycle space is planar if and only if its principal interlacement graph is chordable. © 1981.

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APA

de Fraysseix, H. (1981). Local complementation and interlacement graphs. Discrete Mathematics, 33(1), 29–35. https://doi.org/10.1016/0012-365X(81)90255-7

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