Hamiltonicity of Step-graphon

Xudong Chen

Hamiltonicity of Step-graphon

Probability 2026-01-05 v2 Combinatorics

Authors: Xudong Chen

Abstract

A step-graphon has the strong (resp., weak) $H$ -property if a directed, random graph sampled from it has a Hamilton cycle (resp., a node-wise disjoint cycle cover) asymptotically almost surely. The weak/strong $H$ -property is essentially a zero-one property. We identify key objects associated with the step-graphon that matter for the zero-one law and provide a complete characterization.

Keywords

hamilton cycles

Cite

@article{arxiv.2510.02074,
  title  = {Hamiltonicity of Step-graphon},
  author = {Xudong Chen},
  journal= {arXiv preprint arXiv:2510.02074},
  year   = {2026}
}