{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T20:12:47Z","timestamp":1772136767784,"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>Let $\\mathcal{H}=(H_i\\colon i&lt;\\alpha )$ for some ordinal number $\\alpha$ be an indexed family of graphs. A family $\\mathcal{G}=(G_i\\colon i&lt;\\alpha )$ of edge-disjoint subgraphs of a graph $G$ such that for every $i&lt;\\alpha$: $G_i$ is isomorphic to $H_i$, each $G_i$ is a spanning subgraph of $G$, and $E(G)=\\bigcup\\{E(G_i)\\colon i &lt; \\alpha\\}$ is a $\\mathcal{H}$-factorization of $G$. Let $\\kappa$ be an infinite cardinal. K\u0151nig proved in 1936 that every $\\kappa$-regular graph has a factorization into perfect matchings. We extend this result to the most general factorizations possible. We study indexed families $\\mathcal{T}=(T_i\\colon i&lt;\\kappa)$ of graphs without isolated vertices such that every connected $\\kappa$-regular graph has a $\\mathcal{T}$-factorization. We prove that if $\\mathcal{T}$ is a family of forests each of order at most $\\kappa$, then every connected $\\kappa$-regular graph $G$ has a $\\mathcal{T}$-factorization. These are the most general assumptions for a family $\\mathcal{T}$ for such a statement to hold.<\/jats:p>","DOI":"10.37236\/11536","type":"journal-article","created":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T19:43:58Z","timestamp":1772135038000},"source":"Crossref","is-referenced-by-count":0,"title":["Factorizations of Regular Graphs of Infinite Degree"],"prefix":"10.37236","volume":"33","author":[{"given":"Marcin","family":"Stawiski","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2026,2,13]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p23\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p23\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T19:43:59Z","timestamp":1772135039000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v33i1p23"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,13]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/11536","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,13]]},"article-number":"P1.23"}}