A general criterion for the existence of transversals

R. Aharoni; C. S.J.A. Nash-Williams; S. Shelah

doi:10.1112/plms/s3-47.1.43

A general criterion for the existence of transversals

R. Aharoni
, C. S.J.A. Nash-Williams
, S. Shelah

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

26 Scopus citations

Abstract

We present a necessary and sufficient condition for a family of sets to possess a transversal. Its form follows that of P. Hall’s theorem: a family has a transversal if and only if it does not contain one of a set of ‘forbidden’ substructures.

Original language	English
Pages (from-to)	43-68
Number of pages	26
Journal	Proceedings of the London Mathematical Society
Volume	S3-47
Issue number	1
DOIs	https://doi.org/10.1112/plms/s3-47.1.43
State	Published - Jul 1983

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title = "A general criterion for the existence of transversals",

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author = "R. Aharoni and Nash-Williams, \{C. S.J.A.\} and S. Shelah",

year = "1983",

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AU - Shelah, S.

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AB - We present a necessary and sufficient condition for a family of sets to possess a transversal. Its form follows that of P. Hall’s theorem: a family has a transversal if and only if it does not contain one of a set of ‘forbidden’ substructures.

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A general criterion for the existence of transversals

Abstract

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