{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:56Z","timestamp":1753893836626,"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>Suppose that $t \\ge 2$ is an integer, and randomly label $t$ graphs with the integers $1 \\dots n$. We give sufficient conditions for the number of edges common to all $t$ of the labelings to be asymptotically Poisson as $n \\to \\infty$. We show by example that our theorem is, in a sense, best possible. For $G_n$ a sequence of graphs of bounded degree, each having at most $n$ vertices, Tomescu has shown that the number of spanning trees of $K_n$ having $k$ edges in common with $G_n$ is asymptotically $e^{-2s\/n}(2s\/n)^k\/k! \\times n^{n-2}$, where $s=s(n)$ is the number of edges in $G_n$. As an application of our Poisson-intersection theorem, we extend this result to the case in which maximum degree is only restricted to be ${\\scriptstyle\\cal O}(n \\log\\log n\/\\log n)$. We give an inversion theorem for falling moments, which we use to prove our Poisson-intersection theorem.<\/jats:p>","DOI":"10.37236\/1468","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:00:03Z","timestamp":1578690003000},"source":"Crossref","is-referenced-by-count":1,"title":["Intersections of Randomly Embedded Sparse Graphs are Poisson"],"prefix":"10.37236","volume":"6","author":[{"given":"Edward A.","family":"Bender","sequence":"first","affiliation":[]},{"given":"E. Rodney","family":"Canfield","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[1999,9,26]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1r36\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v6i1r36\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T00:32:13Z","timestamp":1579307533000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v6i1r36"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,9,26]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1999,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1468","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1999,9,26]]},"article-number":"R36"}}