### Jaehoon Kim (김재훈), $K_{r+1}$-saturated graphs with small spectral radius

Room B232 IBS (기초과학연구원)For a graph $H$, a graph $G$ is $H$-saturated if $G$ does not contain $H$ as a subgraph but for any $e\in E(\overline G)$, $G+e$ contains $H$. In this note, we prove a sharp lower bound for the number of paths and walks on length 2 in $n$-vertex $K_{r+1}$-saturated graphs. We then use this bound to give a …