{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,20]],"date-time":"2026-03-20T15:32:11Z","timestamp":1774020731778,"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>We prove inequalities between the densities of various bipartite subgraphs in signed graphs. One of the main inequalities is that the density of any bipartite graph with girth $2r$ cannot exceed the density of the $2r$-cycle. This study is motivated by the Simonovits\u2013Sidorenko conjecture, which states that the density of a bipartite graph $F$ with $m$ edges in any graph $G$ is at least the $m$-th power of the edge density of $G$. Another way of stating this is that the graph $G$ with given edge density minimizing the number of copies of $F$ is, asymptotically, a random graph. We prove that this is true locally, i.e., for graphs $G$ that are \"close\" to a random graph. Both kinds of results are treated in the framework of graphons (2-variable functions serving as limit objects for graph sequences), which in this context was already used by Sidorenko.<\/jats:p>","DOI":"10.37236\/614","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:46:47Z","timestamp":1578714407000},"source":"Crossref","is-referenced-by-count":20,"title":["Subgraph Densities in Signed Graphons and the Local Simonovits&amp;ndash;Sidorenko Conjecture"],"prefix":"10.37236","volume":"18","author":[{"given":"L\u00e1szl\u00f3","family":"Lov\u00e1sz","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,6,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p127\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p127\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:11:04Z","timestamp":1579302664000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p127"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,6,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/614","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011,6,14]]},"article-number":"P127"}}