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A note on the union-closed sets conjecture

  • Giovanni Lo Faro (a1)

Abstract

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.

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References

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[1]A much travelled conjecture’, Austral. Math. Soc. Gaz., 14 (1987), 63.
[2]Norton, R. M. and Sarvate, D. G., ‘Union-closed sets conjecture; some observations’, unpublished manuscript, College of Charleston, 1989.
[3]Renaud, J-C., ‘Is the union-closed sets conjecture the best possible?’, J. Austral. Math. Soc. (ser. A) 51 (1991), 276283.
[4]Sarvate, D. G. and Renaud, J-C., ‘On the union-closed sets conjecture’, Ars Combin. 27 (1989), 149153.
[5]Sarvate, D. G. and Renaud, J-C., ‘Improved bounds for the union-closed sets conjecture’, Ars Combin. 29 (1990), 181185.
[6]Winkler, P., ‘Union-closed sets conjecture’, Austral. Math. Soc. Gaz. 14 (1987), 99.
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A note on the union-closed sets conjecture

  • Giovanni Lo Faro (a1)

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