Forbidding Hamilton cycles in uniform hypergraphs

Abstract

For $1\le d\le \ell <k$, we give a new lower bound for the minimum $d$-degree threshold that guarantees a Hamilton $\ell$-cycle in $k$-uniform hypergraphs. When $k\ge 4$ and $d<\ell =k-1$, this bound is larger than the conjectured minimum $d$-degree threshold for perfect matchings and thus disproves a well-known conjecture of Rödl and Ruciński. Our (simple) construction generalizes a construction of Katona and Kierstead and the space barrier for Hamilton cycles.

6 pages, 0 figure

References in corpus (3)

• Hamilton l-cycles in uniform hypergraphs
• Loose Hamilton cycles in hypergraphs
• Minimum vertex degree conditions for loose Hamilton cycles in $3$-uniform hypergraphs