Neighborly Families of Boxes and Bipartite Coverings

Noga Alon ()
Additional contact information
Noga Alon: Institute for Advanced Study

A chapter in The Mathematics of Paul Erdős II, 2013, pp 15-20 from Springer

Abstract: 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.

Keywords: Bipartite Cover; Neighborhood Family; Complete Bipartite Graph; Standard Box; Distinct Color Classes (search for similar items in EconPapers)
Date: 2013
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4614-7254-4_2

Ordering information: This item can be ordered from
http://www.springer.com/9781461472544

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

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().