activity
20242026
collaborators

6 papers

math.CO2026

Computing the Hamiltonian compression factors of cubic graphs

Marston Conder, Gregor Potocnik, Primoz Potocnik

We present an algorithm for computing Hamiltonian cycles that are invariant under a graph automorphism acting on them as a rotation. We also present an application of this algorith…

math.GR2025

Non-orientable regular maps with negative prime-power Euler characteristic

Marston Conder, Nick Gill, Jozef Širáň

In this paper we provide a classification of all regular maps on surfaces of Euler characteristic for some odd prime and integer . Such maps are necessarily non-…

math.GT2025

Fenchel's conjecture on NEC groups

Emilio Bujalance, F. Javier Cirre, Marston D. E. Conder +1

A classical discovery known as Fenchel's conjecture and proved in the 1950s, shows that every co-compact Fuchsian group has a normal subgroup of finite index isomorphic to the…

math.CO2025

Edge-transitive cubic graphs: Cataloguing and Enumeration

Marston Conder, Primož Potočnik

This paper deals with finite cubic (-regular) graphs whose automorphism group acts transitively on the edges of the graph. Such graphs split into two broad classes, namely arc-t…

math.GR2024

Density of quotient orders in groups and applications to locally-transitive graphs

Marston Conder, Gabriel Verret, Darius Young

We prove that the set of orders of finite quotients of a finitely generated group has natural density 0, 1/2 or 1, and characterise when each of these cases occurs. We apply this t…

math.GR2024

Soluble quotients of triangle groups

Marston D. E. Conder, Darius W. Young

This paper helps explain the prevalence of soluble groups among the automorphism groups of regular maps (at least for `small' genus), by showing that every non-perfect hyperbolic o…