Hang Chen

Counterexamples to two conjectures on the diameter of clique-free graphs

Erd\H{o}s et al. (JCT-B, 1989) conjectured that, for integers $r\ge 2$ and $\delta\ge 2$ with $3r-1\mid\delta$, every connected $K_{2r+1}$-free graph of order $n$ and minimum degree $\delta$ has diameter at most $ \frac{3r-1}{r}\cdot \frac{n}{\delta}+O(1)$. Czabarka et al. (JCT-B, 2021) later proposed the following gen...