2021/07/11 by Fang Tian, Tian, Fang
Computer Science · Mathematics · #05A16 #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2107.04950
openalex publication_date 2021/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For any given integer r\geqslant 3, let k=k(n) be an integer with r\leqslant k\leqslant n. A hypergraph is r-uniform if each edge is a set of r vertices, and is said to be linear if two edges intersect in at most one vertex. Let A1,…,Ak be a given k-partition of [n] with |Ai|=ni\geqslant 1. An r-uniform hypergraph H is called \it k-partite if each edge e satisfies |e∩ Ai|\leqslant 1 for 1\leqslant i\leqslant k. In this paper, the number of linear k-partite r-uniform hypergraphs on n→∞ vertices is determined asymptotically when the number of edges is m(n)=o(n(4)/(3)). For k=n, it is the number of linear r-uniform hypergraphs on vertex set [n] with m=o(n (4)/(3)) edges.