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

## Tuesday, July 13, 2021 @ 4:30 PM - 5:30 PM KST

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 lower bound on the spectral radii of such graphs which is asymptotically tight for each fixed $r$ and $n\to \infty$.