Hamilton cycles in quasirandom hypergraphs

Abstract

We show that, for a natural notion of quasirandomness in $k$-uniform hypergraphs, any quasirandom $k$-uniform hypergraph on $n$ vertices with constant edge density and minimum vertex degree $\Omega (n^{k-1})$ contains a loose Hamilton cycle. We also give a construction to show that a $k$-uniform hypergraph satisfying these conditions need not contain a Hamilton $\ell$-cycle if $k-\ell$ divides $k$. The remaining values of $\ell$ form an interesting open question.

18 pages. Accepted for publication in Random Structures & Algorithms

References in corpus (2)

• Minimum vertex degree conditions for loose Hamilton cycles in $3$-uniform hypergraphs
• Perfect Packings in Quasirandom Hypergraphs II