{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:06Z","timestamp":1753893786151,"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>An element $e$ of a $3$-connected matroid $M$ is elastic if ${\\rm si}(M\/e)$, the simplification of $M\/e$, and ${\\rm co}(M\\backslash e)$, the cosimplification of $M\\backslash e$, are both $3$-connected. It was recently shown that if $|E(M)|\\geq 4$, then $M$ has at least four elastic elements provided $M$ has no $4$-element fans and no member of a specific family of $3$-separators. In this paper, we extend this wheels-and-whirls type result to a splitter theorem, where the removal of elements is with respect to elasticity and keeping a specified $3$-connected minor. We also prove that if $M$ has exactly four elastic elements, then it has path-width three. Lastly, we resolve a question of Whittle and Williams, and show that past analogous results, where the removal of elements is relative to a fixed basis, are consequences of this work.<\/jats:p>","DOI":"10.37236\/11399","type":"journal-article","created":{"date-parts":[[2023,4,21]],"date-time":"2023-04-21T11:34:29Z","timestamp":1682076869000},"source":"Crossref","is-referenced-by-count":0,"title":["A Splitter Theorem for Elastic Elements in 3-Connected Matroids"],"prefix":"10.37236","volume":"30","author":[{"given":"George","family":"Drummond","sequence":"first","affiliation":[]},{"given":"Charles","family":"Semple","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2023,4,21]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i2p12\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v30i2p12\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,21]],"date-time":"2023-04-21T11:34:29Z","timestamp":1682076869000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v30i2p12"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,4,21]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2023,4,7]]}},"URL":"https:\/\/doi.org\/10.37236\/11399","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2023,4,21]]},"article-number":"P2.12"}}