On the sum of sizes of overlapping families

2021/05/02 by Péter Frankl, Jian Wang, Frankl, Peter +1
Mathematics · Social Sciences · #Combinatorics (math.CO) #European history and politics #FOS: Mathematics #Limits and Structures in Graph Theory #Post-Communist Economic and Political Transition

paper · pdf · doi:10.48550/arxiv.2105.00481

openalex publication_date 2021/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let A₁,…,A_m be families of k-subsets of an n-set. Suppose that one cannot choose pairwise disjoint edges from s+1 distinct families. Subject to this condition we investigate the maximum of |A₁|+…+|A_m|. Note that the subcase m=s+1, A₁=…=A_m is the Erdős Matching Conjecture, one of the most important open problems in extremal set theory. We provide some upper bounds, a general conjecture and its solution for the range n≥ 4k²s.

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