1 citations · 1 across the 3 of their papers we have counts for
7 papers
Hamiltonian decompositions of 4-regular Cayley graphs of infinite abelian groups
Joshua Erde, Florian Lehner
A well-known conjecture of Alspach says that every -regular Cayley graph of an abelian group can be decomposed into Hamiltonian cycles. We consider an analogous question for in…
Bounding the cop number of a graph by its genus
Nathan Bowler, Joshua Erde, Florian Lehner +1
It is known that the cop number of a connected graph can be bounded as a function of the genus of the graph . The best known bound, that $c(G) \leq \left\lfloor \f…
Directed path-decompositions
Joshua Erde
Many of the tools developed for the theory of tree-decompositions of graphs do not work for directed graphs. In this paper we show that some of the most basic tools do work in the…
Hamilton decompositions of one-ended Cayley graphs
Joshua Erde, Florian Lehner, Max Pitz
We prove that any one-ended, locally finite Cayley graph with non-torsion generators admits a decomposition into edge-disjoint Hamiltonian (i.e. spanning) double-rays. In particula…
A unified treatment of linked and lean tree-decompositions
Joshua Erde
There are many results asserting the existence of tree-decompositions of minimal width which still represent local connectivity properties of the underlying graph, perhaps the best…
A counterexample to Montgomery's conjecture on dynamic colourings of regular graphs
Nathan Bowler, Joshua Erde, Florian Lehner +3
A \emph{dynamic colouring} of a graph is a proper colouring in which no neighbourhood of a non-leaf vertex is monochromatic. The \emph{dynamic colouring number} of a graph…