2021/04/07 by Balogh, József, Garcia, Ramon I., Li, Lina +1 · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2104.03260
A family of subsets of [n] is intersecting if every pair of its sets intersects. Determining the structure of large intersecting families is a central problem in extremal combinatorics. Frankl-Kupavskii and Balogh-Das-Liu-Sharifzadeh-Tran independently showed that for n≥ 2k + c√(kln k), almost all k-uniform intersecting families are stars. Improving their result, we show that the same conclusion holds for n≥ 2k+ 100ln k. Our proof uses, among others, Sapozhenko's graph container lemma and the Das-Tran removal lemma.