Hamilton cycles in line graphs of 3-hypergraphs

TL;DR

This paper proves that highly connected line graphs derived from rank 3 hypergraphs always contain a Hamilton cycle, extending classical graph results to hypergraph line graphs.

Contribution

It establishes the first Hamiltonicity result for line graphs of hypergraphs with bounded rank beyond ordinary graphs.

Findings

Every 52-connected line graph of a rank 3 hypergraph is Hamiltonian.

First such result for hypergraphs of bounded rank.

Extends classical Hamiltonian cycle results to hypergraph line graphs.

Abstract

We prove that every 52-connected line graph of a rank 3 hypergraph is Hamiltonian. This is the first result of this type for hypergraphs of bounded rank other than ordinary graphs.