{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:42:59Z","timestamp":1753893779685,"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 $A_n$ denote the number of objects of some type  of\"size\" $n$, and let $C_n$ denote the number of these objects which are connected.  It is often the case that there is a relation between a generating function of the $C_n$'s and a generating function of the $A_n$'s. Wright showed that if $\\lim_{n\\rightarrow\\infty} C_n\/A_n =1$, then the radius of convergence of these generating functions must be zero.  In this paper we prove that if the radius of convergence of the generating functions is zero, then $\\limsup_{n\\rightarrow \\infty} C_n\/A_n =1$, proving a conjecture of Compton; moreover, we show that $\\liminf_{n\\rightarrow\\infty} C_n\/A_n$ can assume any value between $0$ and $1$.<\/jats:p>","DOI":"10.37236\/1514","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:03:18Z","timestamp":1578708198000},"source":"Crossref","is-referenced-by-count":3,"title":["When Structures Are Almost Surely Connected"],"prefix":"10.37236","volume":"7","author":[{"given":"Jason P.","family":"Bell","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2000,7,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r36\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r36\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:22:43Z","timestamp":1579324963000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v7i1r36"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,7,20]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2000,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1514","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2000,7,20]]},"article-number":"R36"}}