On a conjecture of Hefetz and Keevash on Lagrangians of intersecting hypergraphs and Turán numbers

2017/01/22 by Biao Wu, Wu, Biao, Yuejian Peng +3
Computer Science · Mathematics · #05C35 #05C65 #Advanced Graph Theory Research #Combinatorics #Combinatorics (math.CO) #Conjecture #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory #Mathematical economics #Mathematics #math.CO #msc:05C35 #msc:05C65

paper · pdf · doi:10.48550/arxiv.1701.06126

25 pages. arXiv admin note: text overlap with arXiv:1307.8423 by other authors

openalex publication_date 2017/01/22 · arxiv created 2017/02/02 · arxiv updated 2017/02/03 · openalex created_date 2017/02/03 · openalex updated_date 2026/07/28

Abstract

Let S^r(n) be the r-graph on n vertices with parts A and B, where the edges consist of all r-tuples with 1 vertex in A and r-1 vertices in B, and the sizes of A and B are chosen to maximise the number of edges. Let M_t^r be the r-graph with t pairwise disjoint edges. Given an r-graph F and a positive integer p≥ |V(F)|, we define the \em extension of F, denoted by H_p^F as follows: Label the vertices of F as v₁,…,v_|V(F)|. Add new vertices v_|V(F)|+1,…,v_p. For each pair of vertices v_i,v_j, 1≤ i

Citations

• Maxima for Graphs and a New Proof of a Theorem of Turán
• Turán numbers of extensions
• Turan numbers of extensions of some sparse hypergraphs via Lagrangians
• A hypergraph Turán theorem via lagrangians of intersecting families

Related

• A Turán theorem for extensions via an Erdős-Ko-Rado theorem for Lagrangians
• Turan numbers of extensions of some sparse hypergraphs via Lagrangians
• Stability and Turán numbers of a class of hypergraphs via Lagrangians
• A hypergraph Turán theorem via lagrangians of intersecting families
• Some Results on Lagrangians of Hypergraphs