Hamilton cycles in 5-connected line graphs

TL;DR

This paper proves that 5-connected line graphs with minimum degree at least 6 are Hamiltonian, extending known results and applying to claw-free graphs and Hamilton-connectedness.

Contribution

It improves the connectivity condition for Hamiltonicity in line graphs from 7-connected to 5-connected with minimum degree at least 6.

Findings

5-connected line graphs with minimum degree ≥6 are Hamiltonian

Extension of Hamiltonicity results to claw-free graphs

Results include Hamilton-connectedness

Abstract

A conjecture of Carsten Thomassen states that every 4-connected line graph is hamiltonian. It is known that the conjecture is true for 7-connected line graphs. We improve this by showing that any 5-connected line graph of minimum degree at least 6 is hamiltonian. The result extends to claw-free graphs and to Hamilton-connectedness.