Hamiltonicity of transitive graphs whose automorphism group has Zp as commutator subgroups

IF 0.7 3区数学 Q2 MATHEMATICS

Discrete Mathematics Pub Date : 2025-09-22 DOI:10.1016/j.disc.2025.114798

Florian Lehner , Farzad Maghsoudi , Babak Miraftab

引用次数: 0

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 X, where the automorphism group of X contains a transitive subgroup G with a cyclic commutator subgroup of prime order.

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自同构群有Zp为交换子群的传递图的哈密性

1982年，Durnberger证明了具有素阶换位子群的有限群的每一个连通Cayley图都包含一个哈密顿循环。本文将这一结果推广到无穷情形。此外，我们将这一结果推广到更广泛的无限图X，其中X的自同构群包含一个传递子群G和一个素数阶的循环换易子群。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Discrete Mathematics 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

424

审稿时长

6 months

期刊介绍： Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory. Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.