{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,12]],"date-time":"2025-09-12T18:50:08Z","timestamp":1757703008460,"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>In this paper, we give a recurrence to enumerate the set $G(n)$ of partitions of a positive even integer $n$ which are the degree sequences of simple graphs.  The recurrence gives rise to an algorithm to compute the number of elements of $G(n)$ in time $O(n^4)$ using space $O(n^3)$. This appears to be the first  method for computing $|G(n)|$ in time bounded by a polynomial in $n$, and it has enabled us to tabulate $|G(n)|$ for even $n \\leq 220$.<\/jats:p>","DOI":"10.37236\/1205","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T01:26:04Z","timestamp":1578705964000},"source":"Crossref","is-referenced-by-count":9,"title":["A Recurrence for Counting Graphical Partitions"],"prefix":"10.37236","volume":"2","author":[{"given":"Tiffany M.","family":"Barnes","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Carla D.","family":"Savage","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[1995,5,18]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v2i1r11\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v2i1r11\/comment","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v2i1r11\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T09:32:00Z","timestamp":1579339920000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v2i1r11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,5,18]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[1995,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1205","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[1995,5,18]]},"article-number":"R11"}}