Hostname: page-component-586b7cd67f-l7hp2 Total loading time: 0 Render date: 2024-11-20T17:46:23.686Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on the union-closed sets conjecture

Part of: Combinatorics

Published online by Cambridge University Press:  09 April 2009

Giovanni Lo Faro
Giovanni Lo Faro
Affiliation:
Dipartimento di Matematica, Università di Messina, Contrada Papardo—Salita Sperone, 31 98166 Sant' Agata, Messina, Italy
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It has been conjectured that for any union-closed set there exists some element which is contained in at least half the sets in . It is shown that this conjecture is true if the number of sets in is less than 25. Several conditions on a counterexample are also obtained.

Keywords

setsunion-closed.

MSC classification

Secondary: 05A05: Permutations, words, matrices 05A99: None of the above, but in this section
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 57 , Issue 2 , October 1994 , pp. 230 - 236
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]‘A much travelled conjecture’, Austral. Math. Soc. Gaz., 14 (1987), 63.Google Scholar
[2]Norton, R. M. and Sarvate, D. G., ‘Union-closed sets conjecture; some observations’, unpublished manuscript, College of Charleston, 1989.Google Scholar
[3]Renaud, J-C., ‘Is the union-closed sets conjecture the best possible?’, J. Austral. Math. Soc. (ser. A) 51 (1991), 276–283.CrossRefGoogle Scholar
[4]Sarvate, D. G. and Renaud, J-C., ‘On the union-closed sets conjecture’, Ars Combin. 27 (1989), 149–153.Google Scholar
[5]Sarvate, D. G. and Renaud, J-C., ‘Improved bounds for the union-closed sets conjecture’, Ars Combin. 29 (1990), 181–185.Google Scholar
[6]Winkler, P., ‘Union-closed sets conjecture’, Austral. Math. Soc. Gaz. 14 (1987), 99.Google Scholar