Hamiltonicity in Cherry-quasirandom 3-graphs

TL;DR

This paper proves that cherry-quasirandom 3-graphs with positive density and large size contain a tight Hamilton cycle, confirming a conjecture and advancing understanding of Hamiltonicity in hypergraphs.

Contribution

It establishes the existence of tight Hamilton cycles in cherry-quasirandom 3-graphs with positive density, solving a previously open conjecture.

Findings

Cherry-quasirandom 3-graphs with positive density have tight Hamilton cycles.

The result holds for sufficiently large graphs with minimum degree proportional to n^2.

Confirms a conjecture by Aigner-Horev and Levy.

Abstract

We show that for any fixed $\alpha>0$, cherry-quasirandom 3-graphs of positive density and sufficiently large order $n$ with minimum vertex degree $\alpha \binom n2$ have a tight Hamilton cycle. This solves a conjecture of Aigner-Horev and Levy.