Rainbow Matchings in r-Partite r-Graphs

@article{Aharoni2009RainbowMI,
  title={Rainbow Matchings in r-Partite r-Graphs},
  author={Ron Aharoni and Eli Berger},
  journal={Electr. J. Comb.},
  year={2009},
  volume={16}
}
Given a collection of matchings M = (M1,M2, . . . ,Mq) (repetitions allowed), a matching M contained in ⋃ M is said to be s-rainbow for M if it contains representatives from s matchings Mi (where each edge is allowed to represent just one Mi). Formally, this means that there is a function φ : M → [q] such that e ∈ Mφ(e) for all e ∈ M , and |Im(φ)| > s. Let f(r, s, t) be the maximal k for which there exists a set of k matchings of size t in some r-partite hypergraph, such that there is no s… CONTINUE READING