A proof of the union-close set conjecture

2017/11/07 by Theophilus Agama, Agama, Theophilus
Computer Science · Engineering · #Computational Geometry and Mesh Generation #FOS: Mathematics #General Mathematics (math.GM) #Optimization and Packing Problems #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.1711.02665

openalex publication_date 2017/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we introduce the notion of the universe, induced communities, and cells with their corresponding spots. Using this language, we formulate and prove the union close set conjecture by showing that for any finite universe \mathbbU and any induced community M_\mathbbU there exist some spot a∈ \mathbbU such that the density D_M_\mathbbU(a)≥ (1)/(2).

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