论文信息 - Neighborly Families of Boxes and Bipartite Coverings

Neighborly Families of Boxes and Bipartite Coverings

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.

Noga Alon | N. Alon

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