A characterization of circle graphs in terms of multimatroid representations

The isotropic matroid M[IAS(G)] of a looped simple graph G is a binary matroid equivalent to the isotropic system of G. In general, M[IAS(G)] is not regular, so it cannot be represented over fields of characteristic not equal 2. The ground set of M[IAS(G)] is denoted W(G); it is partitioned into 3-element subsets corresponding to the vertices of G. When the rank function of M[IAS(G)] is restricted to subtransversals of this partition, the resulting structure is a multimatroid denoted Z(3)(G). In this paper we prove that G is a circle graph if and only if for every field F, there is an F-representable matroid with ground set W(G), which defines Z(3)(G) by restriction. We connect this characterization with several other circle graph characterizations that have appeared in the literature.

Title	A characterization of circle graphs in terms of multimatroid representations
Creator	Brijder, R.
Creator	Traldi, Lorenzo
Publisher	Electronic Journal of Combinatorics
Academic Department	Mathematics
Division	Natural Sciences
Organization	Lafayette College
Date Issued	January 2020
Date Available	2020-03-06
Type	Article
Language	English
Bibliographic Citation	Brijder, R. and L. Traldi (2020 Jan) "A characterization of circle graphs in terms of multimatroid representations." Electronic Journal of Combinatorics 27 (1): P1.25.
Standard Identifier	Handle 10385/dn39x201m
Permalink	http://hdl.handle.net/10385/dn39x201m
Rights Statement	Creative Commons - Attribution
Rights Holders	Brijder, R.
Rights Holders	Traldi, Lorenzo