Dirac-type conditions for spanning bounded-degree hypertrees

Abstract

We prove that for fixed k, every k-uniform hypergraph on n vertices and of minimum codegree at least $n/2+o\left(n\right)$ contains every spanning tight k-tree of bounded vertex degree as a subgraph. This generalises a well-known result of Komlós, Sárközy and Szemerédi for graphs. Our result is asymptotically sharp. We also prove an extension of our result to hypergraphs that satisfy some weak quasirandomness conditions.