Work

Hitting time for loose Hamilton cycles in the random hypergraph process

Year: 2026

Type: preprint

Abstract: The random hypergraph process starts with an empty hypergraph on $n$ vertices and adds a uniformly chosen missing edge at each step. For even $n$, we prove that, with high probability, a $3$-uniform loose Hamilton cycle appears when the last isolated vertex disappears. The approach developed here adapts arguments from Kahn's work on perfect matchings. It can also be extended to obtain the corresponding hitting-time theorems for $r=2$ and every fixed $r\ge4$ satisfying $(r-1)\mid n$. Furthermore, it can be used to estimate the numbers of loose Hamilton cycles at these hitting times for every fixed $r\ge2$, up to a factor of $\exp\{o(n)\}$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.29894

Authors: León, Jared, Liu, Xizhi

Institutions: University of Warwick, University of Science and Technology of China

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: University of Warwick, National Natural Science Foundation of China, University of Science and Technology of China, Division of Mathematical Sciences

OpenAlex ID: W7223231718

Cites: 26

Cited by:

Related to: 10