{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T20:11:00Z","timestamp":1772136660620,"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>The shrinking operation converts a hypergraph into a graph by choosing, from each hyperedge, two endvertices of a corresponding graph edge. A hypertree is a hypergraph which can be shrunk to a tree on the same vertex set. Klimo\u0161ov\u00e1 and Thomass\u00e9 [J. Combin. Theory Ser. B 156 (2022), 250-293] proved (as a tool to obtain their main result on edge-decompositions of graphs into paths of equal length) that any rank $3$ hypertree $T$ can be shrunk to a tree where the degree of each vertex is at least $1\/100$ times its degree in $T$. We prove a stronger and a more general bound, replacing the constant $1\/100$ with $1\/2k$ when the rank is $k$. In place of entropy compression (used by Klimo\u0161ov\u00e1 and Thomass\u00e9), we use a hypergraph orientation lemma combined with a characterisation of edge-coloured graphs admitting rainbow spanning trees.<\/jats:p>","DOI":"10.37236\/12991","type":"journal-article","created":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T19:43:40Z","timestamp":1772135020000},"source":"Crossref","is-referenced-by-count":0,"title":["Hypertree Shrinking Avoiding Low Degree Vertices"],"prefix":"10.37236","volume":"33","author":[{"given":"Karol\u00edna","family":"Hylasov\u00e1","sequence":"first","affiliation":[]},{"given":"Tom\u00e1\u0161","family":"Kaiser","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2026,2,27]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p44\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v33i1p44\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,26]],"date-time":"2026-02-26T19:43:40Z","timestamp":1772135020000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v33i1p44"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,27]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/12991","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,27]]},"article-number":"P1.44"}}