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 $\neq 2$. 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 $\mathcal{Z}_{3}(G)$. In this paper we prove that $G$ is a circle graph if and only if for every field $\mathbb{F}$, there is an $\mathbb{F}$-representable matroid with ground set $W(G)$, which defines $\mathcal{Z}_{3}(G)$ by restriction. We connect this characterization with several other circle graph characterizations that have appeared in the literature.
@article{10_37236_6992,
author = {Robert Brijder and Lorenzo Traldi},
title = {A characterization of circle graphs in terms of multimatroid representations},
journal = {The electronic journal of combinatorics},
year = {2020},
volume = {27},
number = {1},
doi = {10.37236/6992},
zbl = {1431.05032},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6992/}
}
TY - JOUR
AU - Robert Brijder
AU - Lorenzo Traldi
TI - A characterization of circle graphs in terms of multimatroid representations
JO - The electronic journal of combinatorics
PY - 2020
VL - 27
IS - 1
UR - http://geodesic.mathdoc.fr/articles/10.37236/6992/
DO - 10.37236/6992
ID - 10_37236_6992
ER -
%0 Journal Article
%A Robert Brijder
%A Lorenzo Traldi
%T A characterization of circle graphs in terms of multimatroid representations
%J The electronic journal of combinatorics
%D 2020
%V 27
%N 1
%U http://geodesic.mathdoc.fr/articles/10.37236/6992/
%R 10.37236/6992
%F 10_37236_6992
Robert Brijder; Lorenzo Traldi. A characterization of circle graphs in terms of multimatroid representations. The electronic journal of combinatorics, Tome 27 (2020) no. 1. doi: 10.37236/6992
