4 papers
Decomposing edge-coloured complete symmetric digraphs into monochromatic paths
Carl Bürger, Max Pitz
Confirming and extending a conjecture by Guggiari, we show that every countable -edge-coloured complete symmetric digraph containing no directed paths of edge-length $\ell_i…
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…
Hamilton cycles in infinite cubic graphs
Max Pitz
Investigating a problem of B. Mohar, we show that every one-ended Hamiltonian cubic graph with end degree 3 contains a second Hamilton cycle. We also construct two examples showing…
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…