Hamiltonicity of inhomogeneous random graphs
Frederik Garbe, Jan Hladk\'y, Sim\'on Piga
TL;DR
This paper characterizes when inhomogeneous random graphs are almost surely Hamiltonian based on properties of the underlying graphon, extending previous connectivity results with a new geometric condition.
Contribution
It provides a complete characterization of Hamiltonicity in inhomogeneous random graphs through three specific conditions, including a novel geometric obstacle.
Findings
Characterization involves three conditions for Hamiltonicity.
Two conditions relate to graph connectivity, previously established.
A new geometric condition prevents perfect fractional matchings.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.