6 papers
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…
Non-orientable regular maps with negative prime-power Euler characteristic
Marston Conder, Nick Gill, Jozef Å iráÅ
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-…
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…
Edge-transitive cubic graphs: Cataloguing and Enumeration
Marston Conder, Primož PotoÄnik
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…
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…
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…