$H$-Decomposition of $r$-graphs when $H$ is an $r$-graph with exactly $k$ independent edges

Xinmin Hou, Boyuan Liu, Hongliang Lu

Let ${\varphi }_H^r(n)$ be the smallest integer such that, for all $r$-graphs $G$ on $n$ vertices, the edge set $E(G)$ can be partitioned into at most ${\varphi }_H^r(n)$ parts, of which every part…