{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,26]],"date-time":"2026-06-26T00:21:35Z","timestamp":1782433295137,"version":"3.54.5"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We prove Menger-type results in which the obtained paths are pairwise non-adjacent, both for graphs of bounded maximum degree and, more generally, for graphs excluding a topological minor. More precisely, we show the existence of a constant $C$, depending only on the maximum degree or on the forbidden topological minor, such that for any pair of sets of vertices $X,Y$ and any positive integer $k$, there exists either $k$ pairwise non-adjacent $X\\text{-}Y$-paths, or a set of fewer than $Ck$ vertices which separates $X$ and $Y$. We further show better bounds in the subcubic case, and in particular obtain a tight result for two paths using a computer-assisted proof.<\/jats:p>","DOI":"10.37236\/12575","type":"journal-article","created":{"date-parts":[[2024,10,31]],"date-time":"2024-10-31T17:02:01Z","timestamp":1730394121000},"source":"Crossref","is-referenced-by-count":1,"title":["On an Induced Version of Menger's Theorem"],"prefix":"10.37236","volume":"31","author":[{"given":"Kevin","family":"Hendrey","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sergey","family":"Norin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Raphael","family":"Steiner","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J\u00e9r\u00e9mie","family":"Turcotte","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2024,11,1]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i4p28\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i4p28\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,31]],"date-time":"2024-10-31T17:02:01Z","timestamp":1730394121000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v31i4p28"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,1]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,10,3]]}},"URL":"https:\/\/doi.org\/10.37236\/12575","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,11,1]]},"article-number":"P4.28"}}