2012/04/09 by Louis DeBiasio, Tao Jiang, DeBiasio, Louis +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Graph theory and applications #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.1204.1927
openalex publication_date 2012/04/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a 3-graph H, let \ex2(n, H) denote the maximum value of the minimum codegree of a 3-graph on n vertices which does not contain a copy of H. Let F denote the Fano plane, which is the 3-graph \axx',ayy',azz',xyz',xy'z,x'yz,x'y'z'\. Mubayi proved that \ex2(n,F)=(1/2+o(1))n and conjectured that \ex2(n, F)=\floorn/2 for sufficiently large n. Using a very sophisticated quasi-randomness argument, Keevash proved Mubayi's conjecture. Here we give a simple proof of Mubayi's conjecture by using a class of 3-graphs that we call rings. We also determine the Turán density of the family of rings.