Vertex-transitive graphs that have no Hamilton decomposition

TL;DR

This paper proves the existence of infinitely many connected vertex-transitive graphs, including Cayley graphs, that lack Hamilton decompositions, highlighting limitations in Hamiltonian cycle decompositions within symmetric graphs.

Contribution

It demonstrates the existence of infinitely many vertex-transitive graphs without Hamilton decompositions, including Cayley graphs of various valencies, expanding understanding of Hamiltonian properties in symmetric graphs.

Findings

Infinitely many vertex-transitive graphs lack Hamilton decompositions.

Includes Cayley graphs of valency 6 and arbitrarily large valency.

Shows limitations of Hamiltonian cycle decompositions in symmetric graphs.

Abstract

It is shown that there are infinitely many connected vertex-transitive graphs that have no Hamilton decomposition, including infinitely many Cayley graphs of valency 6, and including Cayley graphs of arbitrarily large valency.