2 problems

For odd $k\geq5$, let $H_{n,k}$ be the graph obtained from a clique $K_{\lfloor k/2\rfloor}$ by choosing a vertex $v$, adding $m$ independent vertices adjacent to $v$, and adding…

Let $S_k$ be the star with $k$ vertices, and let $K_r$ be a clique with $r>2$. For $n$ not divisible by $k-1$, the Gan–Loh–Sudakov conjecture. The extremal graph for…