2024/08/16 by Rajko Nenadov, Nenadov, Rajko, Huy Tuan Pham +1
Computer Science · #Combinatorics (math.CO) #Computability, Logic, AI Algorithms #Data Management and Algorithms #FOS: Mathematics #Optimization and Search Problems
paper · pdf · doi:10.48550/arxiv.2408.08514
openalex publication_date 2024/08/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a short and simple proof of the celebrated hypergraph container theorem of Balogh--Morris--Samotij and Saxton--Thomason. On a high level, our argument utilises the idea of iteratively taking vertices of largest degree from an independent set and constructing a hypergraph of lower uniformity which preserves independent sets and inherits edge distribution. The original algorithms for constructing containers also remove in each step vertices of high degree which are not in the independent set. Our modified algorithm postpones this until the end, which surprisingly results in a significantly simplified analysis.