10-tough chordal graphs are Hamiltonian

TL;DR

This paper proves that every 10-tough chordal graph is Hamiltonian and Hamilton-connected, improving previous bounds and employing hypergraph extension of Hall's Theorem as the main tool.

Contribution

It establishes a lower toughness bound for Hamiltonicity in chordal graphs, advancing the understanding of graph toughness and Hamiltonian properties.

Findings

Every 10-tough chordal graph is Hamiltonian.

Every 10-tough chordal graph is Hamilton-connected.

Uses hypergraph extension of Hall's Theorem as a key method.

Abstract

Chen et al. proved that every 18-tough chordal graph has a Hamilton cycle [Networks 31 (1998), 29-38]. Improving upon their bound, we show that every 10-tough chordal graph is Hamiltonian (in fact, Hamilton-connected). We use Aharoni and Haxell's hypergraph extension of Hall's Theorem as our main tool.