{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:40Z","timestamp":1753893820230,"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>The aim of this paper is to provide an affirmative answer to a recent question by Bubeck and Linial on the local profile of trees. For a tree $T$, let $p^{(k)}_1(T)$ be the proportion of paths among all $k$-vertex subtrees (induced connected subgraphs) of $T$, and let $p^{(k)}_2(T)$ be the proportion of stars. Our main theorem states: if $p^{(k)}_1(T_n) \\to 0$ for a sequence of trees $T_1,T_2,\\ldots$ whose size tends to infinity, then $p^{(k)}_2(T_n) \\to 1$. Both are also shown to be equivalent to the statement that the number of $k$-vertex subtrees grows superlinearly and the statement that the $(k-1)$th degree moment grows superlinearly.<\/jats:p>","DOI":"10.37236\/5943","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T19:29:04Z","timestamp":1578684544000},"source":"Crossref","is-referenced-by-count":1,"title":["Paths vs. Stars in the Local Profile of Trees"],"prefix":"10.37236","volume":"24","author":[{"given":"\u00c9va","family":"Czabarka","sequence":"first","affiliation":[]},{"given":"L\u00e1szl\u00f3","family":"Sz\u00e9kely","sequence":"additional","affiliation":[]},{"given":"Stephan","family":"Wagner","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2017,2,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i1p22\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v24i1p22\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:05:50Z","timestamp":1579237550000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v24i1p22"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,2,3]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2017,1,20]]}},"URL":"https:\/\/doi.org\/10.37236\/5943","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2017,2,3]]},"article-number":"P1.22"}}