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On Hamilton cycles in quasiprimitive graphs of order 2pq
Abstract
Let p>q>5 be primes. We determine the socles and corresponding actions of quasiprimitive imprimitive groups of degree 2pq, all of which are almost simple. Using this classification, we prove that a connected graph of order 2pq admitting a quasiprimitive automorphism group contains a Hamilton cycle, except possibly for three specified families of actions with socle PSL(2,p) or PSL(2,q2).
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BibTeX
@misc{yu2026hamilton,
title = {{On Hamilton cycles in quasiprimitive graphs of order $2pq$}},
author = {Hao Yu and Tianlei Zhou},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35976},
eprint = {2610.35976},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35976},
}
RIS
TY - UNPB
TI - On Hamilton cycles in quasiprimitive graphs of order 2pq
AU - Hao Yu
AU - Tianlei Zhou
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35976
UR - https://arxiv.org/abs/2610.35976
AB - Let p>q>5 be primes. We determine the socles and corresponding actions of quasiprimitive imprimitive groups of degree 2pq, all of which are almost simple. Using this classification, we prove that a connected graph of order 2pq admitting a quasiprimitive automorphism group contains a Hamilton cycle, except possibly for three specified families of actions with socle PSL(2,p) or PSL(2,q^2).
ER -