Neighborly Families of Boxes and Bipartite Coverings

  • Noga Alon
Part of the Algorithms and Combinatorics book series (AC, volume 14)


A bipartite covering of order k of the complete graph K n on n vertices is a collection of complete bipartite graphs so that every edge of K n lies in at least 1 and at most k of them. It is shown that the minimum possible number of subgraphs in such a collection is Θ(kn 1/k ). This extends a result of Graham and Pollak, answers a question of Felzenbaum and Perles, and has some geometric consequences. The proofs combine combinatorial techniques with some simple linear algebraic tools.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Noga Alon
    • 1
    • 2
  1. 1.Institute for Advanced StudyPrincetonUSA
  2. 2.Department of MathematicsTel Aviv UniversityTel AvivIsrael

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