Monochromatic Path and Cycle Partitions in Hypergraphs

@article{Gyrfs2013MonochromaticPA,
  title={Monochromatic Path and Cycle Partitions in Hypergraphs},
  author={Andr{\'a}s Gy{\'a}rf{\'a}s and G{\'a}bor N. S{\'a}rk{\"o}zy},
  journal={Electr. J. Comb.},
  year={2013},
  volume={20},
  pages={P18}
}
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… CONTINUE READING

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