Odd-Sunflowers

Frankl, Péter and Pach, János and Pálvölgyi, Dömötör (2023) Odd-Sunflowers. In: Proceedings of the 12th European Conference on Combinatorics, Graph Theory and Applications. Masaryk University, Brno, pp. 441-449. ISBN 978-80-280-0344-9

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Abstract

Extending the notion of sunflowers, we call a family of at least two sets an \emph{odd-sunflower} if every element of the underlying set is contained in an odd number of sets or in none of them. It follows from the Erd\H os--Szemer\'edi conjecture, recently proved by %Alweiss, Lovett, Wu, and Zhang, Naslund and Sawin, that there is a constant such that every family of subsets of an -element set that contains no odd-sunflower consists of at most sets. We construct such families of size at least 1.5021n.

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