{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:10Z","timestamp":1753893850381,"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>Let $r$, $m$, and $n$ be positive integers such that $rm=n$.  For each $i \\in \\{1, \\ldots, m\\}$ let $B_i = \\{r(i-1)+1, \\ldots, ri\\}$.  The $r$-block connectivity of a tree on $n$ labelled vertices is the vertex connectivity of the graph obtained by collapsing the vertices in $B_i$, for each $i,$ to a single (pseudo-)vertex $v_i$. In this paper we prove that, for fixed values of $r$, with $r \\geq 2$, the $r$-block connectivity of a random tree on $n$ vertices, for large values of $n$, is likely to be either $r-1$ or $r$, and furthermore that $r-1$ is the right answer for a constant fraction of all trees on $n$ vertices.<\/jats:p>","DOI":"10.37236\/97","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:36:42Z","timestamp":1578699402000},"source":"Crossref","is-referenced-by-count":0,"title":["The Block Connectivity of Random Trees"],"prefix":"10.37236","volume":"16","author":[{"given":"Andrew R. A.","family":"McGrae","sequence":"first","affiliation":[]},{"given":"Michele","family":"Zito","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,1,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r8\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r8\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T22:14:34Z","timestamp":1579299274000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,1,7]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/97","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,1,7]]},"article-number":"R8"}}