On the Turán number of the expansion of the t-fan

2025/05/16 by Cheng Xin, Cheng, Xin, Dániel Gerbner +5
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2505.11105

openalex publication_date 2025/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30

Abstract

The t-fan is the graph on 2t+1 vertices consisting of t triangles which intersect at exactly one common vertex. For a given graph F, the r-expansion F^r of F is the r-uniform hypergraph obtained from F by adding r-2 distinct new vertices to each edge of F. We determine the Turán number of the 3-expansion of the t-fan for sufficiently large n.

Citations

• Generalized Turán results for disjoint cliques
• The maximum number of triangles in F_k-free graphs
• The Turán number of Berge book hypergraphs
• Generalized Turán problems for disjoint copies of graphs
• Tur'an numbers for Berge-hypergraphs and related extremal problems
• A survey of Turán problems for expansions

Related

• Turán numbers of extensions
• The linear Turán number of the k-fan
• A survey of Turán problems for expansions
• Turan numbers of extensions of some sparse hypergraphs via Lagrangians
• The Turán number of Berge book hypergraphs