The largest $K_r$-free set of vertices in a random graph

Tom Bohman, Marcus Michelen, Dhruv Mubayi

For $r\ge 2$ and a graph $G$, let ${\alpha }_r(G)$ be the maximum number of vertices in a $K_r$-free subgraph of $G$. We investigate the value ${\alpha }_r(G)$ when $G$ is the random graph $G…