© 2018 Wiley Periodicals, Inc. We show that any complete k-partite graph G on n vertices, with k≥3, whose edges are two-coloured, can be covered with two vertex-disjoint monochromatic paths of distinct colours, given that ...

Extending a result of Rado to hypergraphs, we prove that for all s,k,t is an element of N$$s, k, t \in {\mathbb {N}}$$\end{document} with k >= t >= 2 the vertices of every r=s(k-t+1)-edge-coloured countably infinite complete ...

We show that for any 2-local colouring of the edges of the balanced complete bipartite graph Kn,n, its vertices can be covered with at most 3 disjoint monochromatic paths. And, we can cover almost all vertices of any ...

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 ...