Name
Abstract | ||
|---|---|---|
The codegree threshold ex2(n, F) of a non-empty 3-graph F is the minimum d = d(n) such that every 3-graph on n vertices in which every pair of vertices is contained in at least d+1 edges contains a copy of F as a subgraph. We study ex2(n, F) when F=K4−, the 3-graph on 4 vertices with 3 edges. Using flag algebra techniques, we prove thatex2(n,K4−)=n4+O(1). This settles in the affirmative a conjecture of Nagle [Nagle, B., Turán-Related Problems for Hypergraphs, Congr. Numer. (1999), 119–128]. In addition, we obtain a stability result: for every near-extremal configuration G, there is a quasirandom tournament T on the same vertex set such that G is close in the edit distance to the 3-graph C(T) whose edges are the cyclically oriented triangles from T. For infinitely many values of n, we are further able to determine ex2(n,K4−) exactly and to show that tournament-based constructions C(T) are extremal for those values of n. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1016/j.endm.2017.06.067 | Electronic Notes in Discrete Mathematics |
Keywords | Field | DocType |
extremal combinatorics,hypergraphs,codegree treshold,flag algebras | Discrete mathematics,Combinatorics,Vertex (geometry),Constraint graph,Extremal combinatorics,Mathematics | Journal |
Volume | ISSN | Citations |
61 | 1571-0653 | 1 |
PageRank | References | Authors |
0.35 | 8 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Victor Falgas-Ravry | 1 | 28 | 7.46 |
| Oleg Pikhurko | 2 | 318 | 47.03 |
| Emil R. Vaughan | 3 | 40 | 3.49 |
| Jan Volec | 4 | 40 | 8.27 |