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Neighborly Families of Boxes and Bipartite Coverings

  • Noga AlonEmail author
Chapter

Summary

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 \(\Theta (k{n}^{1/k})\). 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 Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institute for Advanced StudyPrincetonUSA
  2. 2.Tel Aviv UniversityTel AvivIsrael

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