On Hamilton cycles in quasiprimitive graphs of order $2pq$

Hao Yu; Tianlei Zhou

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arXiv · 2610.35976

On Hamilton cycles in quasiprimitive graphs of order $2pq$

Hao Yu·Tianlei Zhou

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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 $\PSL(2,q^2)$.

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Hao Yu, Tianlei Zhou. 2026-10-26. On Hamilton cycles in quasiprimitive graphs of order $2pq$. https://arxiv.org/abs/2610.35976

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