A Hypergraph Version of a Graph Packing Theorem by Bollobás and Eldridge


  • Contract grant sponsor: NSF; Contract grant number: DMS-0965587; Contract grant sponsor: Russian Foundation for Basic Research; Contract grant number: 09-01-00244.


Two n-vertex hypergraphs G and H pack, if there is a bijection math formula such that for every edge math formula, the set math formula is not an edge in H. Extending a theorem by Bollobás and Eldridge on graph packing to hypergraphs, we show that if math formula and n-vertex hypergraphs G and H with math formula with no edges of size 0, 1, math formula and n do not pack, then either

  1. one of G and H contains a spanning graph-star, and each vertex of the other is contained in a graph edge, or
  2. one of G and H has math formula edges of size math formula not containing a given vertex, and for every vertex x of the other hypergraph some edge of size math formula does not contain x.