2013/05/23 by Ran Gu, Xueliang Li, Gu, Ran +3
Computer Science · Mathematics · #05C35 #05C65 #05D05 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.1305.5372
openalex publication_date 2013/05/23 · openalex created_date 2016/11/30 · openalex updated_date 2026/07/28
The Turán number of a k-uniform hypergraph H, denoted by exk(n;H ), is the maximum number of edges in any k-uniform hypergraph F on n vertices which does not contain H as a subgraph. Let Cℓ(k ) denote the family of all k-uniform minimal cycles of length ℓ, S(ℓ1,…,ℓr) denote the family of hypergraphs consisting of unions of r vertex disjoint minimal cycles of length ℓ1,…,ℓr, respectively, and ℂℓ(k ) denote a k-uniform linear cycle of length ℓ. We determine precisely exk(n;S(ℓ1,…,ℓr) ) and exk(n;ℂℓ1(k ), …, ℂℓr(k ) ) for sufficiently large n. The results extend recent results of Füredi and Jiang who determined the Turán numbers for single k-uniform minimal cycles and linear cycles.