{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:30Z","timestamp":1753893810318,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"3","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>If $G$ is a looped graph, then its adjacency matrix represents a binary matroid $M_{A}(G)$ on $V(G)$. $M_{A}(G)$ may be obtained from the delta-matroid represented by the adjacency matrix of $G$, but $M_{A}(G)$ is less sensitive to the structure of $G$. Jaeger proved that every binary matroid is $M_{A}(G)$ for some $G$ [Ann. Discrete Math. 17 (1983), 371-376]. The relationship between the matroidal structure of $M_{A}(G)$ and the graphical structure of $G$ has many interesting features. For instance, the matroid minors $M_{A}(G)-v$ and $M_{A}(G)\/v$ are both of the form $M_{A}(G^{\\prime}-v)$ where $G^{\\prime}$ may be obtained from $G$ using local complementation. In addition, matroidal considerations lead to a principal vertex tripartition, analogous in some ways to the principal edge tripartition of Rosenstiehl and Read [Ann. Discrete Math. 3 (1978), 195-226]. Several of these results are given two very different proofs, the first involving linear algebra and the second involving set systems or delta-matroids. Also, the Tutte polynomials of the adjacency matroids of $G$ and its full subgraphs are closely connected to the interlace polynomial of Arratia, Bollob\u00e1s and Sorkin [Combinatorica 24 (2004), 567-584].<\/jats:p>","DOI":"10.37236\/2911","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:22:51Z","timestamp":1578705771000},"source":"Crossref","is-referenced-by-count":4,"title":["The Adjacency Matroid of a Graph"],"prefix":"10.37236","volume":"20","author":[{"given":"Lorenzo","family":"Traldi","sequence":"first","affiliation":[]},{"given":"Robert","family":"Brijder","sequence":"additional","affiliation":[]},{"given":"Hendrik Jan","family":"Hoogeboom","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,8,30]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i3p27\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i3p27\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:14:07Z","timestamp":1579259647000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i3p27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,8,30]]},"references-count":0,"journal-issue":{"issue":"3","published-online":{"date-parts":[[2013,7,19]]}},"URL":"https:\/\/doi.org\/10.37236\/2911","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,8,30]]},"article-number":"P27"}}