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Keywords:

  • graph packing;
  • hypergraph

Abstract

Two n-vertex hypergraphs G and H pack, if there is a bijection inline image such that for every edge inline image, the set inline image is not an edge in H. Extending a theorem by Bollobás and Eldridge on graph packing to hypergraphs, we show that if inline image and n-vertex hypergraphs G and H with inline image with no edges of size 0, 1, inline image 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 inline image edges of size inline image not containing a given vertex, and for every vertex x of the other hypergraph some edge of size inline image does not contain x.