"Jednoduchost je velká ctnost, ale vyžaduje mnoho práce, aby jí bylo dosaženo, a vzdělání, aby byla oceněna. A co je horší: složitost se lépe prodává." - E. W. Dijkstra
As a variant on the traditional Ramsey-type questions, there has been a lot of research about the existence of spanning monochromatic subgraphs in complete edge-coloured graphs and hypergraphs. One of the central questions in this area was proposed by Lehel around 1979, who conjectured that the vertex set of every 2-edge-coloured complete graph can be partitioned into two monochromatic cycles of distinct colours. This was answered in the affirmative by Bessy and Thomassé in 2010. We generalise the question of Lehel to the setting of 3-uniform hypergraphs (3-graphs). More precisely, we show that every sufficiently large 2-edge-coloured complete 3-graph admits a vertex partition into two monochromatic tight cycles, possibly of the same colour. We also present examples showing that (in contrast to the graph case) it is not always possible to find partitions into two monochromatic tight cycles of different colours. As by-products from our proof, we can find vertex partitions into two cycles of different colours and two vertices, and vertex partitions into a cycle and a path of different colours. This is joint work with Frederik Garbe, Richard Mycroft, Richard Lang and Allan Lo.
