Hamilton cycles in dense vertex-transitive graphs

TL;DR

This paper proves that dense, large vertex-transitive graphs always contain Hamilton cycles and provides a polynomial-time algorithm to find them, confirming Lovász's conjecture in this case.

Contribution

It establishes the existence of Hamilton cycles in dense, large vertex-transitive graphs and offers a polynomial-time algorithm for finding such cycles.

Findings

Dense, large vertex-transitive graphs contain Hamilton cycles

Polynomial-time algorithm for finding Hamilton cycles in these graphs

Confirms Lovász's conjecture for dense, large cases

Abstract

A famous conjecture of Lov\'asz states that every connected vertex-transitive graph contains a Hamilton path. In this article we confirm the conjecture in the case that the graph is dense and sufficiently large. In fact, we show that such graphs contain a Hamilton cycle and moreover we provide a polynomial time algorithm for finding such a cycle.