Hamilton Cycles in Semisymmetric Graphs
Abstract
In light of Lov\'{a}sz's longstanding question on the existence of Hamilton paths in vertex-transitive graphs, this paper considers a natural variant: what if vertex-transitivity is relaxed, yet a high degree of symmetry--specifically edge-transitivity--is retained? To investigate this, we focus on the class of semisymmetric graphs, which are regular, edge-transitive, but not vertex-transitive. In this paper, it will be shown that every connected semisymmetric graph of order , where and are two distinct primes contains a Hamilton cycle and that every connected cubic semisymmetric graph of order less than 3000 contains a Hamilton cycle too. Based on these observations, the following question is posed: construct a connected semisymmetric graph which has no Hamilton cycle.
Keywords
Cite
@article{arxiv.2602.14388,
title = {Hamilton Cycles in Semisymmetric Graphs},
author = {Shaofei Du and Kai Yuan},
journal= {arXiv preprint arXiv:2602.14388},
year = {2026}
}