{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,29]],"date-time":"2026-05-29T19:29:10Z","timestamp":1780082950745,"version":"3.54.0"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"2","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Extremal problems concerning the number of independent sets or complete subgraphs in a graph have been well studied in recent years. Cutler and Radcliffe proved that among graphs with $n$ vertices and maximum degree at most $r$, where $n = a(r+1)+b$ and $0 \\le b \\le r$, $aK_{r+1}\\cup K_b$ has the maximum number of complete subgraphs, answering a question of Galvin. Gan, Loh, and Sudakov conjectured that $aK_{r+1}\\cup K_b$ also maximizes the number of complete subgraphs $K_t$ for each fixed size $t \\ge 3$, and proved this for $a = 1$. Cutler and Radcliffe proved this conjecture for $r \\le 6$.   We investigate a variant of this problem where we fix the number of edges instead of the number of vertices. We prove that $aK_{r+1}\\cup {\\mathcal C}(b)$, where ${\\mathcal C}(b)$ is the colex graph on $b$ edges, maximizes the number of triangles among graphs with $m$ edges and any fixed maximum degree $r\\le 8$, where $m = a \\binom{r+1}{2} + b$ and $0 \\le b &lt; \\binom{r+1}{2}$.<\/jats:p>","DOI":"10.37236\/7343","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T07:13:55Z","timestamp":1578640435000},"source":"Crossref","is-referenced-by-count":7,"title":["Many Triangles with Few Edges"],"prefix":"10.37236","volume":"26","author":[{"given":"Rachel","family":"Kirsch","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"A. J.","family":"Radcliffe","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"23455","published-online":{"date-parts":[[2019,5,31]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i2p36\/7850","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v26i2p36\/7850","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T04:12:40Z","timestamp":1579234360000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v26i2p36"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,5,31]]},"references-count":0,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2019,4,5]]}},"URL":"https:\/\/doi.org\/10.37236\/7343","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,5,31]]},"article-number":"P2.36"}}