Skip to content
DraconiticResearch
Search Sources API
182,544 studies31 sourcesUpdated 30 min ago
PreprintarXiv licencearXiv

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

  • Zhou Tianlei
Open at sourcePDFDOICite

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.

Related

  1. Multi-Way Expansion, Laplacian Gaps, and Imprimitivity in Vertex-Transitive Graphs
    Zejun Huang, Chenxi Yang
    HALPreprintLicence Ouverte 2.0Full textGeneral mathematicsHAL
  2. Vertex-transitive strongly regular graphs in the switching class of doubly transitive two-graphs
    Robert F. Bailey, Gábor P. Nagy, Valentino Smaldore
    arXivPreprintCC BY 4.0Full textAlgebra & number theoryCombinatorics & discrete mathematicsarXiv
  3. Enumeration of small vertex-transitive directed strongly regular graphs
    A. E. Brouwer, Š. Gyürki
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  4. Linear circumference in vertex-transitive graphs
    Jie Ma, Ziyuan Zhao
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  5. Counting Minimal Vertex Cutsets and a Gap at 1 for Site Percolation on Vertex-Transitive Graphs
    Joel Bassil
    arXivPreprintCC BY 4.0Full textProbabilityarXiv

Cite

BibTeXRIS
BibTeX
@misc{tianlei2026hamilton,
  title = {{On Hamilton cycles in connected vertex-transitive graphs of order $2pq$}},
  author = {Zhou Tianlei},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.02349},
  eprint = {2608.02349},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.02349},
}
RIS
TY  - UNPB
TI  - On Hamilton cycles in connected vertex-transitive graphs of order 2pq
AU  - Zhou Tianlei
PY  - 2026
DA  - 2026/10/13
PB  - arXiv
DO  - 10.48550/arxiv.2608.02349
UR  - https://arxiv.org/abs/2608.02349
AB  - 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.
ER  -