Hamiltonicity of inhomogeneous random graphs
Combinatorics
2026-04-02 v1
Abstract
We provide a complete characterization of those graphons for which the inhomogeneous random graph is asymptotically almost surely Hamiltonian. The characterization involves three conditions. Two of them constitute the characterization of being a.a.s. connected, as was shown recently by Hladk\'y and Viswanathan. The third condition captures a geometric obstacle which prevents from having perfect fractional matchings.
Keywords
Cite
@article{arxiv.2604.00899,
title = {Hamiltonicity of inhomogeneous random graphs},
author = {Frederik Garbe and Jan Hladký and Simón Piga},
journal= {arXiv preprint arXiv:2604.00899},
year = {2026}
}
Comments
32 pages, 2 figure