A characterization of circle graphs in terms of total unimodularity. (May 2022)

• Record Type: Journal Article
• Authors: Brijder, Robert; Traldi, Lorenzo
• Is Part Of: European journal of combinatorics. Volume 102(2022)
• Publication Date: 2022-05
• Subjects: Combinatorial analysis -- Periodicals; Analyse combinatoire -- Périodiques; Combinatorial analysis; Periodicals; Electronic journals; 511.6
• DOI: 10.1016/j.ejc.2021.103455
• Languages: English
• ISSNs: 0195-6698

Abstract

Abstract: A graph G has an associated multimatroid Z 3 ( G ), which is equivalent to the isotropic system of G studied by Bouchet. In previous work it was shown that G is a circle graph if and only if for every field F, the rank function of Z 3 ( G ) can be extended to the rank function of an F -representable matroid. In the present paper we strengthen this result using a multimatroid analogue of total unimodularity. As a consequence we obtain a characterization of matroid planarity in terms of this total-unimodularity analogue.