{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T07:45:30Z","timestamp":1780386330518,"version":"3.54.1"},"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>Given graphs $G_1,\\ldots,G_s$ all on a common vertex set and a graph $H$ with $e(H) = s$, a copy of $H$ is transversal or rainbow if it contains one edge from each $G_i$. We establish a stability result for transversal Hamilton cycles: the minimum degree required to guarantee a transversal Hamilton cycle can be lowered as long as the graph collection $G_1,\\ldots,G_n$ is far in edit distance from several extremal cases. We obtain an analogous result for Hamilton paths. The proof is a combination of our newly developed regularity-blow-up method for transversals, along with the absorption method.<\/jats:p>","DOI":"10.37236\/13624","type":"journal-article","created":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T17:13:43Z","timestamp":1762190023000},"source":"Crossref","is-referenced-by-count":2,"title":["Stability of Transversal Hamilton Cycles and Paths"],"prefix":"10.37236","volume":"32","author":[{"given":"Yangyang","family":"Cheng","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Katherine","family":"Staden","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2025,11,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i4p36\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v32i4p36\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,3]],"date-time":"2025-11-03T17:13:43Z","timestamp":1762190023000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v32i4p36"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,11,3]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2025,10,3]]}},"URL":"https:\/\/doi.org\/10.37236\/13624","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,11,3]]},"article-number":"P4.36"}}