Feng-Ming Dong

A Tur\'an-type extremal problem for the number of spanning trees in $C_4$-free graphs

For a graph \(F\), the Tur\'an number \(\ex(n,F)\) is the maximum number of edges in an \(F\)-free graph on \(n\) vertices. Let \(q\ge 2\) be an integer and set \(n=q^{2}+q+1\). Brown and Erd\H{o}s, R\'enyi and S\'os independently proved that $\ex(n,C_{4})\ge \frac12 q(q+1)^{2}$ for every prime power \(q\), and F\"ured...