{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:42:52Z","timestamp":1753893772777,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>A split system on a multiset $\\mathcal M$ is a multiset of bipartitions of $\\mathcal M$. Such a split system $\\mathfrak S$ is compatible if it can be represented by a tree in such a way that the vertices of the tree are labelled by the elements in $\\mathcal M$, the removal of each edge in the tree yields a bipartition in $\\mathfrak S$ by taking the labels of the two resulting components, and every bipartition in $\\mathfrak S$ can be obtained from the tree in this way. Compatibility of split systems is a key concept in phylogenetics, and compatible split systems have applications to, for example, multi-labelled phylogenetic trees. In this contribution, we present a novel characterization for compatible split systems, and for split systems admitting a unique representation by a tree. In addition, we show that a conjecture on compatibility stated in 2008 holds for some large classes of split systems.<\/jats:p>","DOI":"10.37236\/10974","type":"journal-article","created":{"date-parts":[[2024,12,17]],"date-time":"2024-12-17T20:54:23Z","timestamp":1734468863000},"source":"Crossref","is-referenced-by-count":0,"title":["Compatible Split Systems on a Multiset"],"prefix":"10.37236","volume":"31","author":[{"given":"Vincent","family":"Moulton","sequence":"first","affiliation":[]},{"given":"Guillaume","family":"Scholz","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2024,12,17]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i4p63\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v31i4p63\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,12,17]],"date-time":"2024-12-17T20:54:23Z","timestamp":1734468863000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v31i4p63"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,17]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,10,3]]}},"URL":"https:\/\/doi.org\/10.37236\/10974","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2024,12,17]]},"article-number":"P4.63"}}