On Hamilton cycles in connected vertex-transitive graphs of order 2pq

2026/08/03 by Zhou Tianlei
Mathematics · #math.CO

paper · pdf

arxiv created 2026/08/03 · arxiv updated 2026/08/04

Abstract

The existence of Hamilton cycles in connected vertex-transitive graphs is a core open problem in algebraic graph theory, originating from Lovász's 1969 conjecture. All connected vertex-transitive graphs of order pq are known to be Hamiltonian except the Petersen graph, and primitive graph of order 2pq are resolved except the Coxeter graph. This paper considers connected vertex-transitive graphs of order 2pq where every transitive automorphism subgroup admits a maximal intransitive normal subgroup inducing prime-length orbits. We prove that all such graphs contain a Hamilton cycle, with no new exceptions beyond the already characterized non-qualifying graphs. This result covers a large non-quasiprimitive graphs of order 2pq, advancing the full resolution of the 2pq.

Citations

• Hamilton Cycles In Vertex-Transitive Graphs of Order 10p
• Hamilton cycles in vertex-transitive graphs of order 6p
• Hamilton Cycles In Primitive Graphs of Order 2rs
• Cayley graphs on groups with commutator subgroup of order 2p are hamiltonian
• Odd-order Cayley graphs with commutator subgroup of order pq are hamiltonian
• Cayley graphs on nilpotent groups with cyclic commutator subgroup are hamiltonian
• Hamilton Paths and Cycles in Vertex-Transitive Graphs of Order 6p
• Hamiltonicity of Vertex-Transitive Graphs of Order 4p