Proof of Lov\'{a}sz conjecture for odd order

TL;DR

This paper proves Lovász's conjecture that all connected vertex-transitive graphs with an odd number of vertices contain a Hamilton path, by analyzing their structure and establishing Hamiltonicity.

Contribution

The paper introduces a structural characterization of odd-order connected vertex-transitive graphs and proves they always contain a Hamilton path, confirming Lovász's conjecture.

Findings

Connected vertex-transitive graphs with odd order are Hamiltonian.

Structural insights enable the proof of Hamiltonicity for these graphs.

Confirms Lovász's conjecture for graphs of odd order.

Abstract

Lov\'{a}sz conjectured that every connected vertex-transitive graph contains a hamilton path in 1970. First we reveal the structure of connected vertex-transitive graphs with an odd number of vertices. Then we prove that every connected vertex-transitive graph with an odd number of vertices is hamiltonian.