2022/01/19 by Hongkui Wang, Xinmin Hou, Wang, Hongkui +1
Computer Science · Mathematics · #05D05 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2201.07510
openalex publication_date 2022/01/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given an irreducible fraction (c)/(d) ∈ [0,1], a pair (A,B) is called a (c)/(d)-cross-intersecting pair of 2[n] if A, B are two families of subsets of [n] such that for every pair A \inA and B\inB, |A ∩ B|= (c)/(d)|B|. Mathew, Ray, and Srivastava [\it\small Fractional cross intersecting families, Graphs and Comb., 2019] proved that |A||B|≤ 2n if (A, B) is a (c)/(d)-cross-intersecting pair of 2[n] and characterized all the pairs (A,B) with |A||B|=2n, such a pair also is called a maximal \frac cd-cross-intersecting pair of 2[n], when \frac cd∈\0,\frac12, 1\. In this note, we characterize all the maximal \frac cd-cross-intersecting pairs (A,B) when 0