{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T20:29:42Z","timestamp":1776198582795,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $\\mathcal{F}$ be a set of subsets of a set $W$. When is there a tree $T$ with vertex set $W$ such that each member of $\\mathcal{F}$ is the set of vertices of a subtree of $T$? It is necessary that $\\mathcal{F}$ has the Helly property and the intersection graph of $\\mathcal{F}$ is chordal. We will show that these two necessary conditions are together sufficient in the finite case, and more generally, they are sufficient if no element of $W$ belongs to infinitely many infinite sets in $\\mathcal{F}$.<\/jats:p>","DOI":"10.37236\/14646","type":"journal-article","created":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T19:28:40Z","timestamp":1776194920000},"source":"Crossref","is-referenced-by-count":0,"title":["The Vertex Sets of Subtrees of a Tree"],"prefix":"10.37236","volume":"33","author":[{"given":"Maria","family":"Chudnovsky","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tung","family":"Nguyen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alex","family":"Scott","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Paul","family":"Seymour","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2026,4,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i2p7\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i2p7\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T19:29:43Z","timestamp":1776194983000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v33i2p7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4,14]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,4,14]]}},"URL":"https:\/\/doi.org\/10.37236\/14646","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4,14]]},"article-number":"P2.7"}}