Advancing the Rödl Nibble: New bounds on matchings and the list chromatic index of hypergraphs

Stephen Gould, Tom Kelly

Let $H$ be a $(k+1)$-uniform hypergraph which is nearly $D$-regular, such that any set of $i$ vertices is contained in at most $D_i$ edges of $H$ for each $i=2,3,\dots ,k+1$. I…