Vol. 10, No. 1, 2021

Download this article
Download this article For screen
For printing
Recent Issues
Volume 10, Issue 1
Volume 9, Issue 4
Volume 9, Issue 3
Volume 9, Issue 2
Volume 9, Issue 1
Volume 8, Issue 4
Volume 8, Issue 3
Volume 8, Issue 2
Volume 8, Issue 1
The Journal
About the Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
founded and published with the
scientific support and advice of the
Moscow Institute of
Physics and Technology
ISSN (electronic): 2640-7361
ISSN (print): 2220-5438
Previously Published
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Shattered matchings in intersecting hypergraphs

Peter Frankl and János Pach

Vol. 10 (2021), No. 1, 49–59

Let X be an n-element set, where n is even. We refute a conjecture of J. Gordon and Y. Teplitskaya, according to which, for every maximal intersecting family of n 2 -element subsets of X, one can partition X into n 2 disjoint pairs in such a way that no matter how we pick one element from each of the first n 2 1 pairs, the set formed by them can always be completed to a member of by adding an element of the last pair.

The above problem is related to classical questions in extremal set theory. For any t 2, we call a family of sets 2X t-separable if there is a t-element subset T X such that for every ordered pair of elements (x,y) of T, there exists F such that F {x,y} = {x}. For a fixed t, 2 t 5, and n , we establish asymptotically tight estimates for the smallest integer s = s(n,t) such that every family with || s is t-separable.

PDF Access Denied

However, your active subscription may be available on Project Euclid at

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

extremal set theory, shattered set, matching, Vapnik–Chervonenkis dimension, separability
Mathematical Subject Classification
Primary: 05C65, 05D05, 05D40
Received: 10 May 2020
Revised: 27 July 2020
Accepted: 12 August 2020
Published: 16 January 2021
Peter Frankl
Rényi Institute
Hungarian Academy of Sciences
János Pach
Rényi Institute
Hungarian Academy of Sciences