Shicai Gong

Minimizing the number of edges in $\mathcal{C}_{[4,6]}$-saturated graphs

Let $\mathcal{C}_{[4,r]}$ be the family of cycles $\{C_4, \dots, C_r\}$. A graph $G$ is said to be $\mathcal{C}_{[4,r]}$-saturated if $G$ does not contain a copy of cycle $C_i$ for $4\le i\le r$, but the addition of any edge $e\notin E(G)$ creates at least one copy of $C_i$ for $4\le i\le r.$ The saturation number $sat...