Neighborly families of boxes and bipartite coverings

Noga Alon

doi:10.1007/978-1-4614-7254-4_2

Neighborly families of boxes and bipartite coverings

Noga Alon

Research output: Chapter in Book/Report/Conference proceeding › Chapter

1 Scopus citations

Abstract

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.

Original language	English (US)
Title of host publication	The Mathematics of Paul Erdos II, Second Edition
Publisher	Springer New York
Pages	15-20
Number of pages	6
ISBN (Electronic)	9781461472544
ISBN (Print)	9781461472537
DOIs	https://doi.org/10.1007/978-1-4614-7254-4_2
State	Published - Jan 1 2013
Externally published	Yes

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/978-1-4614-7254-4_2

Cite this

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Neighborly families of boxes and bipartite coverings

Abstract

All Science Journal Classification (ASJC) codes

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