A tight bound on {C3,C5}-free connected graphs with positive Lin-Lu-Yau Ricci curvature

We prove that any simple $\{C_3,C_5\}$-free non-empty connected graph $G$ with LLY curvature bounded below by $\kappa>0$ has the order at most $2^{\frac{2}{\kappa}}$. This upper bound is achieved if and only if $G$ is a hypercube $Q_d$ and $\kappa=\frac{2}{d}$ for some integer $d\geq 1$. This is joint work with E.G.K.M.Gamlath, Xiaonan Liu, and Linyuan Lu.