Let G be a graph on n vertices with maximum degree ?. We use the Lovasz local lemma to show the following two results about colourings ? of the edges of the complete graph Kn. If for each vertex v of Kn the colouring ? ...

Given a c-edge-coloured multigraph, where c is a positive integer, a proper Hamiltonian path is a path that contains all the vertices of the multigraph such that no two adjacent edges have the same colour. In this work we ...

We investigated effects of fruit colour (red, black or white), habitat (anthropogenic edges and forest interior) and fragment size on the removal of artificial fruits in semideciduous forests in south-east Brazil. Eight ...

The first part of this thesis concerns monochromatic cycle partitions. We make the following three contributions. Our first result is that for any colouring of the edges of the complete bipartite graph $K_{n,n}$ with 3 ...

We prove that the list chromatic index of a graph of maximum degree Delta and treewidth <= root 2 Delta -3 is Delta; and that the total chromatic number of a graph of maximum degree and treewidth <= Delta/3+1 is Delta+1. ...

It is shown that Halin graphs are -edge-choosable and that graphs of tree-width 3 are -edge-choosable and -total-colourable.