Triangles in $C_5$-free graphs and Hypergraphs of Girth Six

Abstract

We introduce a new approach and prove that the maximum number of triangles in a $C_5$-free graph on $n$ vertices is at most $$(1+o(1))\frac{1}{3\sqrt{2}}{n}^{3/2}.$$ We also show a connection to $r$-uniform hypergraphs without (Berge) cycles of length less than six, and estimate their maximum possible size.

arXiv comment14 pages