{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:53Z","timestamp":1753893833954,"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>The triangle removal lemma states that a simple graph with $o(n^3)$ triangles can be made triangle-free by removing $o(n^2)$ edges. It is natural to ask if this widely used result can be extended to multi-graphs. In this short paper we rule out the possibility of such an extension by showing that there are multi-graphs with only $n^{2+o(1)}$ triangles that are still far from being triangle-free. On the other hand, we show that for some slowly growing function $g(n)=\\omega(1)$, if a multi-graph has only $g(n)n^2$ triangles then it must be close to being triangle-free. The proof relies on variants of the Ruzsa-Szemer\u00e9di theorem.<\/jats:p>","DOI":"10.37236\/249","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:32:44Z","timestamp":1578717164000},"source":"Crossref","is-referenced-by-count":0,"title":["Multigraphs (Only) Satisfy a Weak Triangle Removal Lemma"],"prefix":"10.37236","volume":"16","author":[{"given":"Asaf","family":"Shapira","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Raphael","family":"Yuster","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2009,3,20]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1n11\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1n11\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T03:05:16Z","timestamp":1579316716000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1n11"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,3,20]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/249","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,3,20]]},"article-number":"N11"}}