Monochromatic Path and Cycle Partitions in Hypergraphs

Here we address the problem to partition edge colored hypergraphs by monochromatic paths and cycles generalizing a well-known similar problem for graphs. We show that r-colored r-uniform complete hypergraphs can be partitioned into monochromatic Berge-paths of distinct colors. Also, apart from 2k − 5 vertices, 2-colored k-uniform hypergraphs can be partitioned into two monochromatic loose paths. In general, we prove that in any r coloring of a k-uniform hypergraph there is a partition of the vertex set into monochromatic loose cycles such that their number depends only on r and k.