Unavoidable subprojections in union-closed set systems of infinite breadth

Choi, Yemon and Ghandehari, Mahya and Pham, Hung Le (2021) Unavoidable subprojections in union-closed set systems of infinite breadth. European Journal of Combinatorics, 94. ISSN 0195-6698

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We consider union-closed set systems with infinite breadth, focusing on three particular configurations ${\mathcal T}_{\rm max}(E)$, ${\mathcal T}_{\rm min}(E)$ and ${\mathcal T}_{\rm ort}(E)$. We show that these three configurations are not isolated examples; in any given union-closed set system of infinite breadth, at least one of these three configurations will occur as a subprojection. This characterizes those union-closed set systems which have infinite breadth, and is the first general structural result for such set systems.

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Journal Article
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European Journal of Combinatorics
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This is the author’s version of a work that was accepted for publication in European Journal of Combinatorics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in European Journal of Combinatorics, 94, 2021 DOI: 10.1016/j.ejc.2021.103311
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18 Jan 2021 10:10
Last Modified:
09 Aug 2022 00:25