Hall's marriage theorem

Peter J. Cameron

doi:10.1112/jlms.70378

Hall's marriage theorem

Peter J. Cameron^*

^*Corresponding author for this work

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

Abstract

In 1935, Philip Hall published what is often referred to as ‘Hall's marriage theorem’ in a short paper (P. Hall, J. Lond. Math. Soc. (1) 10 (1935), no. 1, 26–30.) This paper has been very influential. I state the theorem and outline Hall's proof, together with some equivalent (or stronger) earlier results, and proceed to discuss some the many directions in combinatorics and beyond which this theorem has influenced.

Original language	English
Article number	e70378
Number of pages	9
Journal	Journal of the London Mathematical Society
Volume	113
Issue number	1
Early online date	6 Jan 2026
DOIs	https://doi.org/10.1112/jlms.70378
Publication status	Published - Jan 2026

Keywords

Representatives of subsets
SDRs
Hall's condition
Matroids
Infinite families

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Cameron_2026_JLMS_Halls-marriage-theorem_CC
© 2026 The Author(s). This is an open access article under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
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Cite this

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KW - Matroids

KW - Infinite families

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Hall's marriage theorem

Abstract

Keywords

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