{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:45:10Z","timestamp":1759063510248,"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>We study edge-decompositions of highly connected graphs into copies of a given tree.\u00a0In particular we attack the following conjecture by Bar\u00e1t and Thomassen:\u00a0for each tree $T$, there exists a natural\u00a0number $k_T$ such that if $G$ is a\u00a0$k_T$-edge-connected graph, and $|E(T)|$ divides $|E(G)|$,\u00a0then $E(G)$ has a decomposition into copies of $T$.\u00a0As one of our main results it is sufficient to prove the conjecture for bipartite graphs.\u00a0The same result has been independently obtained by Carsten Thomassen (2013).Let $Y$ be the unique tree with degree sequence $(1,1,1,2,3)$.\u00a0We prove that if $G$ is a $191$-edge-connected graph of size divisible by $4$, then $G$\u00a0has a $Y$-decomposition.\u00a0This is the first instance of such a theorem, in which the tree is different from a path or a star.\u00a0Recently Carsten Thomassen proved a more general decomposition theorem for bistars, which yields the same result with a worse constant.<\/jats:p>","DOI":"10.37236\/2110","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:08:24Z","timestamp":1578704904000},"source":"Crossref","is-referenced-by-count":10,"title":["Edge-Decomposition of Graphs into Copies of a Tree with Four Edges"],"prefix":"10.37236","volume":"21","author":[{"given":"J\u00e1nos","family":"Bar\u00e1t","sequence":"first","affiliation":[]},{"given":"D\u00e1niel","family":"Gerbner","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2014,3,17]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i1p55\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v21i1p55\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:01:57Z","timestamp":1579258917000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v21i1p55"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,3,17]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2014,1,13]]}},"URL":"https:\/\/doi.org\/10.37236\/2110","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2014,3,17]]},"article-number":"P1.55"}}