{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,15]],"date-time":"2026-03-15T14:16:18Z","timestamp":1773584178261,"version":"3.50.1"},"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 a recent conjecture of Beisegel et al. that for every positive integer $k$, every graph containing an induced $P_k$ also contains an avoidable $P_k$. Avoidability generalises the notion of simpliciality best known in the context of chordal graphs. The conjecture was only established for $k \\in \\{1,2\\}$ (Ohtsuki et al. 1976, and Beisegel et al. 2019, respectively). Our result also implies a result of Chv\u00e1tal et al. 2002, which assumed cycle restrictions.\u00a0 We provide a constructive and elementary proof, relying on a single trick regarding the induction hypothesis. In the line of previous works, we discuss conditions for multiple avoidable paths to exist.<\/jats:p>","DOI":"10.37236\/9030","type":"journal-article","created":{"date-parts":[[2020,12,15]],"date-time":"2020-12-15T08:21:42Z","timestamp":1608020502000},"source":"Crossref","is-referenced-by-count":6,"title":["Avoidable Paths in Graphs"],"prefix":"10.37236","volume":"27","author":[{"given":"Marthe","family":"Bonamy","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Oscar","family":"Defrain","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Meike","family":"Hatzel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jocelyn","family":"Thiebaut","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2020,12,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p46\/8227","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i4p46\/8227","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,12,15]],"date-time":"2020-12-15T08:21:42Z","timestamp":1608020502000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i4p46"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12,11]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2020,10,2]]}},"URL":"https:\/\/doi.org\/10.37236\/9030","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12,11]]},"article-number":"P4.46"}}