On a conjecture of Stein

Ron Aharoni; Eli Berger; Dani Kotlar; Ran Ziv

doi:10.1007/s12188-016-0160-3

On a conjecture of Stein

Ron Aharoni
, Eli Berger
, Dani Kotlar
, Ran Ziv

Department of Mathematics

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

Abstract

Stein (Pac J Math 59:567–575, 1975) proposed the following conjecture: if the edge set of K_n _, _n is partitioned into n sets, each of size n, then there is a partial rainbow matching of size n- 1. He proved that there is a partial rainbow matching of size n(1-Dnn!), where D_n is the number of derangements of [n]. This means that there is a partial rainbow matching of size about (1-1e)n. Using a topological version of Hall’s theorem we improve this bound to 23n.

Original language	English
Pages (from-to)	203-211
Number of pages	9
Journal	Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg
Volume	87
Issue number	2
DOIs	https://doi.org/10.1007/s12188-016-0160-3
State	Published - 1 Oct 2017

Bibliographical note

Publisher Copyright:
© 2016, The Author(s).

Keywords

Rainbow matchings
Ryser’s Latin Square conjecture
Transversals

ASJC Scopus subject areas

General Mathematics

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10.1007/s12188-016-0160-3

Cite this

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AU - Kotlar, Dani

AU - Ziv, Ran

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N2 - Stein (Pac J Math 59:567–575, 1975) proposed the following conjecture: if the edge set of Kn , n is partitioned into n sets, each of size n, then there is a partial rainbow matching of size n- 1. He proved that there is a partial rainbow matching of size n(1-Dnn!), where Dn is the number of derangements of [n]. This means that there is a partial rainbow matching of size about (1-1e)n. Using a topological version of Hall’s theorem we improve this bound to 23n.

AB - Stein (Pac J Math 59:567–575, 1975) proposed the following conjecture: if the edge set of Kn , n is partitioned into n sets, each of size n, then there is a partial rainbow matching of size n- 1. He proved that there is a partial rainbow matching of size n(1-Dnn!), where Dn is the number of derangements of [n]. This means that there is a partial rainbow matching of size about (1-1e)n. Using a topological version of Hall’s theorem we improve this bound to 23n.

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KW - Transversals

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On a conjecture of Stein

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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