{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:46:40Z","timestamp":1759063600666,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A proper edge coloring of a graph $G$ with  colors $1,2,3,\\dots$ is called an interval coloring if the colors on the edges incident with any  vertex are consecutive. A bipartite graph is $(3,4)$-biregular if all vertices in one part have degree $3$ and all vertices in the other part have  degree $4$. Recently it was proved  [J. Graph Theory 61 (2009), 88-97] that if such a graph $G$ has a spanning subgraph whose components are  paths with endpoints at  3-valent vertices and lengths in $\\{2, 4, 6, 8\\}$,  then $G$ has an interval coloring. It was also conjectured that every simple $(3,4)$-biregular  bipartite graph has such a subgraph. We provide some evidence for this conjecture by proving that a simple $(3,4)$-biregular bipartite graph has a spanning subgraph whose components are nontrivial paths with endpoints at $3$-valent vertices and lengths not exceeding $22$.<\/jats:p>","DOI":"10.37236\/705","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:39:42Z","timestamp":1578713982000},"source":"Crossref","is-referenced-by-count":2,"title":["A Note on Path Factors of $(3,4)$-Biregular Bipartite Graphs"],"prefix":"10.37236","volume":"18","author":[{"given":"Carl Johan","family":"Casselgren","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2011,11,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p218\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p218\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:59:07Z","timestamp":1579301947000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p218"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,11,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/705","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,11,14]]},"article-number":"P218"}}