Hamiltonicity of Transitive Graphs Whose Automorphism Group Has $\Z_{p}$ as Commutator Subgroups
Combinatorics
2024-12-12 v1
Abstract
In 1982, Durnberger proved that every connected Cayley graph of a finite group with a commutator subgroup of prime order contains a hamiltonian cycle. In this paper, we extend this result to the infinite case. Additionally, we generalize this result to a broader class of infinite graphs , where the automorphism group of contains a transitive subgroup with a cyclic commutator subgroup of prime order.
Keywords
Cite
@article{arxiv.2412.08105,
title = {Hamiltonicity of Transitive Graphs Whose Automorphism Group Has $\Z_{p}$ as Commutator Subgroups},
author = {Florian Lehner and Farzad Maghsoudi and Babak Miraftab},
journal= {arXiv preprint arXiv:2412.08105},
year = {2024}
}
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