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Rein van der Hout, Kees Roos, Some results and conjectures related to Frankl’s union closed conjecture

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DOI: 10.23952/jano.8.2026.1.02
Volume 8, Issue 1, 1 April 2026, Pages 11-18

 

Abstract. A union-closed family F is a finite collection of distinct subsets of a finite set such that the union of two subsets in F belongs to F. Péter Frankl conjectured in 1979 that, for any such family, there exists an element that belongs to at least half of its sets. This conjecture is still unsolved. In this paper, we present some results and conjectures related to Frankl’s conjecture. The new conjectures are based on evidence provided by some experimental results.

 

How to Cite this Article:
R. van der Hout, K. Roos, Some results and conjectures related to Frankl’s union closed conjecture, J. Appl. Numer. Optim. 8 (2026), 11-18.