5 citations · 32 across the 42 of their papers we have counts for
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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…
Isoperimetry in integer lattices
Ben Barber, Joshua Erde
The edge isoperimetric problem for a graph is to determine, for each , the minimum number of edges leaving any set of vertices. In general this problem is NP-hard, but e…
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…