Minimum codegree threshold for Hamilton l-cycles in k-uniform hypergraphs

Abstract

For $1\le \ell <k/2$, we show that for sufficiently large $n$, every $k$-uniform hypergraph on $n$ vertices with minimum codegree at least $\frac{n}{2(k-\ell )}$ contains a Hamilton $\ell$-cycle. This codegree condition is best possible and improves on work of Hàn and Schacht who proved an asymptotic result.

22 pages, 0 figure. Accepted for publication in JCTA. arXiv admin note: text overlap with arXiv:1307.3693