© 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 ...

We show that any 2-colouring of the 3-uniform complete hypergraph Kn (3) on n vertices contains two disjoint monochromatic tight cycles of distinct colours covering all but o(n) vertices of Kn (3). The same result holds ...

© 2018 Wiley Periodicals Inc. We show that for every η > 0 there exists an integer n 0 such that every 2-coloring of the 3-uniform complete hypergraph on n ≥ n 0 vertices contains two disjoint monochromatic tight cycles ...

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 coloring of the edges of the complete bipartite graph Kn,n with three colors there are five disjoint monochromatic cycles which together cover all but o(n) of the vertices. In the same situation, 18 ...

Confirming a conjecture of Gyarfas, we prove that, for all natural numbers k and r, the vertices of every r-edge-colored complete k-uniform hypergraph can be partitioned into a bounded number (independent of the size of ...

We show that for all l, k, n with l <= k/2 and (k-l) dividing n the following hypergraph-variant of Lehel's conjecture is true. Every 2-edge-colouring of the k-uniform complete hypergraph kappa((k))(n) on n vertices has ...

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 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 main focus of this thesis is the study of monochromatic cycle partitions in uniform hypergraphs. The first part deals with Berge-cycles. Extending a result of Rado to hypergraphs, we prove that for all $r,k \in \N$ ...