2p³阶半对称图的哈密顿圈
Hamilton cycles of semisymmetric graphs of order $2p^3$
浏览论文内容
中文总结 AI 辅助
该研究在Du和Yuan关于2pq阶半对称图含哈密顿圈的结论基础上，进一步证明任意素数p对应的2p³阶连通半对称图均含哈密顿圈。
中文摘要 AI 辅助
针对Lovász关于顶点传递图中哈密顿路径存在性的长期问题，Du和Yuan考虑了一个自然变体：若放宽顶点传递性，同时保留高度对称性——具体为边传递性，会怎样？为研究此问题，他们研究半对称图（即正则、边传递但非顶点传递的图），并证明每个阶为2pq（p、q为不同素数）的连通半对称图都包含哈密顿圈。本文证明，对于任意素数p，每个阶为2p³的连通半对称图也包含哈密顿圈。
英文摘要
In light of Lovász's longstanding question on the existence of Hamilton paths in vertex-transitive graphs, Du and Yuan considered a natural variant: what if vertex-transitivity is relaxed, while a high degree of symmetry--specifically edge-transitivity--is retained? To investigate this, they studied semisymmetric graphs (i.e. regular, edge-transitive, but not vertex-transitive graphs) and showed that every connected semisymmetric graph of order $2pq$, where $p$ and $q$ are distinct primes, contains a Hamilton cycle. In this paper, it is shown that for any prime $p$, every connected semisymmetric graph of order $2p^3$ also contains a Hamilton cycle.
