{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T18:28:34Z","timestamp":1773080914804,"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>Given graphs $G$ and $H$ and a positive number $b$, a weighted $(H,b)$-decomposition of $G$ is a partition of the edge set of $G$ such that each part is either a single edge or forms an $H$-subgraph. We assign a weight of $b$ to each $H$-subgraph in the decomposition and a weight of 1 to single edges. The total weight of the decomposition is the sum of the weights of all elements in the decomposition. Let $\\phi(n,H,b)$ be the the smallest number such that any graph $G$ of order $n$ admits an $(H,b)$-decomposition with weight at most $\\phi(n,H,b)$. The value of the function $\\phi(n,H,b)$ when $b=1$ was determined, for large $n$, by Pikhurko and Sousa [Minimum $H$-Decompositions of Graphs, Journal of Combinatorial Theory, B, 97 (2007), 1041\u20131055.]  Here we determine the asymptotic value of $\\phi(n,H,b)$ for any fixed bipartite graph $H$ and any value of $b$ as $n$ tends to infinity.<\/jats:p>","DOI":"10.37236\/613","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:46:50Z","timestamp":1578714410000},"source":"Crossref","is-referenced-by-count":1,"title":["Minimum Weight $H$-Decompositions of Graphs: The Bipartite Case"],"prefix":"10.37236","volume":"18","author":[{"given":"Teresa","family":"Sousa","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,6,6]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p126\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p126\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:11:13Z","timestamp":1579302673000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p126"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,6,6]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/613","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,6,6]]},"article-number":"P126"}}