{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T03:18:20Z","timestamp":1773112700640,"version":"3.50.1"},"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 $\\{P_{2},P_{5}\\}$-factor of a graph is a spanning subgraph of the graph each of whose components is isomorphic to either $P_{2}$ or $P_{5}$, where $P_{n}$ denote the path of order $n$.\u00a0In this paper, we show that if a graph $G$ satisfies $c_{1}(G-X)+\\frac{2}{3}c_{3}(G-X)\\leq \\frac{4}{3}|X|+\\frac{1}{3}$ for all $X\\subseteq V(G)$, then $G$ has a $\\{P_{2},P_{5}\\}$-factor, where $c_{i}(G-X)$ is the number of components $C$ of $G-X$ with $|V(C)|=i$.\u00a0Moreover, it is shown that above condition is sharp.<\/jats:p>","DOI":"10.37236\/5817","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T15:37:34Z","timestamp":1578670654000},"source":"Crossref","is-referenced-by-count":16,"title":["The Existence of a Path-Factor without Small Odd Paths"],"prefix":"10.37236","volume":"25","author":[{"given":"Yoshimi","family":"Egawa","sequence":"first","affiliation":[]},{"given":"Michitaka","family":"Furuya","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2018,3,2]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p40\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v25i1p40\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:38:17Z","timestamp":1579235897000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v25i1p40"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3,2]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2018,1,12]]}},"URL":"https:\/\/doi.org\/10.37236\/5817","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3,2]]},"article-number":"P1.40"}}