2 problems

Let $q>r\geq 2$ and let a girth-$g$ decomposition mean a $K_q^r$-decomposition containing no configuration of the forbidden size below $g$. High Girth Existence Conjecture. For eve…

Let $q\geq 3$, let $G$ be a graph on $n$ vertices, and let $\delta^*_{K_q}$ denote the fractional $K_q$-decomposition threshold. A graph is $K_q$-divisible when its divisibility co…