{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:20:28Z","timestamp":1758824428720,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>If $\\mathcal{S}$ is a set of matroids, then the matroid $M$ is $\\mathcal{S}$-fragile if, for every element $e\\in E(M)$,\u00a0either $M\\backslash e$ or $M\/e$ has no minor isomorphic to a member of $\\mathcal{S}$.\u00a0Excluded-minor characterizations often depend, implicitly or explicitly, on understanding classes of fragile matroids. In certain cases, when $\\mathcal{M}$ is a minor-closed class of $\\mathcal{S}$-fragile matroids, and $N\\in \\mathcal{M}$, the only members of $\\mathcal{M}$ that contain $N$ as a minor\u00a0are obtained from $N$ by increasing the length of fans.\u00a0We prove that if this is the case, then we can certify\u00a0it with a finite case-analysis.\u00a0The analysis \u00a0involves examining matroids that are\u00a0at most two elements larger than $N$.<\/jats:p>","DOI":"10.37236\/3994","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T18:59:24Z","timestamp":1578682764000},"source":"Crossref","is-referenced-by-count":2,"title":["Fan-Extensions in Fragile Matroids"],"prefix":"10.37236","volume":"22","author":[{"given":"Carolyn","family":"Chun","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Deborah","family":"Chun","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dillon","family":"Mayhew","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefan H. M.","family":"Van Zwam","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2015,5,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i2p30\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i2p30\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:17:09Z","timestamp":1579238229000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i2p30"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,5,22]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2015,4,14]]}},"URL":"https:\/\/doi.org\/10.37236\/3994","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,5,22]]},"article-number":"P2.30"}}