{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,1]],"date-time":"2025-10-01T16:15:44Z","timestamp":1759335344419,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>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.<\/jats:p>","DOI":"10.37236\/6992","type":"journal-article","created":{"date-parts":[[2020,1,24]],"date-time":"2020-01-24T04:18:50Z","timestamp":1579839530000},"source":"Crossref","is-referenced-by-count":2,"title":["A Characterization of Circle Graphs in Terms of Multimatroid Representations"],"prefix":"10.37236","volume":"27","author":[{"given":"Robert","family":"Brijder","sequence":"first","affiliation":[]},{"given":"Lorenzo","family":"Traldi","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2020,1,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p25\/8011","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p25\/8011","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,24]],"date-time":"2020-01-24T04:18:51Z","timestamp":1579839531000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i1p25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,24]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/6992","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,1,24]]},"article-number":"P1.25"}}