{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,11]],"date-time":"2026-03-11T13:30:12Z","timestamp":1773235812340,"version":"3.50.1"},"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 degree partition of a simple graph is its degree sequence  rearranged in weakly decreasing order. The polytope of degree partitions  (respectively, degree sequences) is the convex hull of degree partitions  (respectively, degree sequences) of all simple graphs on the vertex set  $[n]$. The polytope of degree sequences has been very well studied. In  this paper we study the polytope of degree partitions. We show that adding  the inequalities $x_1\\geq x_2 \\geq \\cdots \\geq x_n$ to a linear inequality  description of the degree sequence polytope yields a linear inequality  description of the degree partition polytope and we show that the   extreme points of the degree partition polytope are the  $2^{n-1}$ threshold partitions (these are precisely those extreme points  of the degree sequence polytope that have weakly decreasing coordinates). We also show that the degree partition polytope has $2^{n-2}(2n-3)$ edges  and $(n^2 -3n + 12)\/2$ facets, for $n\\geq 4$. Our main tool is an averaging  transformation on real sequences defined by repeatedly averaging over the  ascending runs.<\/jats:p>","DOI":"10.37236\/1072","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T05:00:32Z","timestamp":1578718832000},"source":"Crossref","is-referenced-by-count":7,"title":["The Polytope of Degree Partitions"],"prefix":"10.37236","volume":"13","author":[{"given":"Amitava","family":"Bhattacharya","sequence":"first","affiliation":[]},{"given":"S.","family":"Sivasubramanian","sequence":"additional","affiliation":[]},{"given":"Murali K.","family":"Srinivasan","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,5,5]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r46\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r46\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:11:07Z","timestamp":1579320667000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1r46"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,5,5]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1072","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,5,5]]},"article-number":"R46"}}