We study conjectures relating degree conditions in 3-partite hypergraphs to the matching number of the hypergraph, and use topological methods to prove special cases. In particular, we prove a strong version of a theorem of Drisko  (as generalized by the first two authors ), that every family of 2n-1 matchings of size n in a bipartite graph has a partial rainbow matching of size n. We show that milder restrictions on the sizes of the matchings suffice. Another result that is strengthened is a theorem of Cameron and Wanless , that every n×n Latin square has a generalized diagonal (set of n entries, each in a different row and column) in which no symbol appears more than twice. We show that the same is true under the weaker condition that the square is row-Latin.
Bibliographical noteFunding Information:
Contract grant sponsor: BSF; contract grant number: 2006099; contract grant sponsor: ISF; contract grant number: 1581/12; contract grant sponsor: Technion's research promotion fund; contract grant sponsor: Discont Bank chair.
© 2017 Wiley Periodicals, Inc.
- 3-partite hypergraphs
ASJC Scopus subject areas
- Geometry and Topology
- Discrete Mathematics and Combinatorics