发表机构
Capital Normal University（首都师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对阶为$2pq$且满足特定自同构子群条件的连通点传递图，证明其均含哈密顿圈，为解决代数图论中相关公开问题提供了重要进展。
AI 中文摘要
连通点传递图中的哈密顿圈存在性是代数图论的核心公开问题，源于Lovász在1969年提出的猜想。目前已知所有阶为$pq$的连通点传递图除Petersen图外均为哈密顿图，阶为$2pq$的本原图除Coxeter图外已解决。本文研究阶为$2pq$的连通点传递图，其每个传递自同构子群都存在极大非传递正规子群，诱导素数长度的轨道。我们证明所有这类图都包含哈密顿圈，除已明确的不符合条件的图外无新的例外。该结果覆盖了大量阶为$2pq$的拟本原图，推进了$2pq$情形的完全解决。
英文摘要
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 $2pq$.
