For a hypergraph H let β(H) denote the minimal number of edges from H covering V(H). An edge S of H is said to represent fairly (resp. almost fairly) a partition (V1, V2, …, Vm) of for all i ≤ m. In matroids any partition of V(H) can be represented fairly by some independent set. We look for classes of hypergraphs H in which any partition of V(H) can be represented almost fairly by some edge.We show that this is true when H is the set of independent sets in a path, and conjecture that it is true when H is the set of matchings in Kn;n. We prove that partitions of E(Kn;n) into three sets can be represented almost fairly. The methods of proofs are topological.
|Title of host publication||A Journey through Discrete Mathematics|
|Subtitle of host publication||A Tribute to Jiri Matousek|
|Publisher||Springer International Publishing|
|Number of pages||28|
|State||Published - 1 Jan 2017|
Bibliographical notePublisher Copyright:
© Springer International Publishing AG 2017.
ASJC Scopus subject areas
- Computer Science (all)
- Mathematics (all)
- Economics, Econometrics and Finance (all)
- Business, Management and Accounting (all)