Local complementation and interlacement graphs

Citations of this article
Mendeley users who have this article in their library.


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.




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

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free