Set systems without a simplex, Helly hypergraphs and union-efficient families

2022/10/28 by Cambie, Stijn, Salia, Nika
#05C35 #05C65 #05C69 #05D05 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2210.16211

Abstract

We present equivalent formulations for concepts related to set families for which every subfamily with empty intersection has a bounded sub-collection with empty intersection. Hereby, we summarize the progress on the related questions about the maximum size of such families. In this work we solve a boundary case of a problem of Tuza for non-trivial q-Helly families, by applying Karamata's inequality and determining the minimum size of a 2-self-centered graph for which the common neighborhood of every pair of vertices contains a clique of size q-2.

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