The size and number of Turan hypergraphs for 3-uniform H
Complete hypergraphs
H=K4
| N | ex(H,N) | Number of Turan graphs |
| 4 | 3 | 1 |
H=K5
| N | ex(H,N) | Number of Turan graphs |
| 5 | 9 | 1 |
H=K6
| N | ex(H,N) | Number of Turan graphs |
| 6 | 19 | 1 |
Other 3-uniform hypergraphs
H=K4-
This is the unique hypergraph obtained by removing an edge from the
3-uniform K4.
The Turan hypergraphs.
| N | ex(H,N) | Number of Turan graphs |
| 6 | 10 | 1 |
| 7 | 15 | 1 |
| 8 | 22 | 5 |
| 9 | 32 | 6 |
| 10 | 44 | 43 |
| 11 | 60 | 1 |
| 12 | 80 | 1 |
| 13 | 101 | 1 |
| 14 | 126 | 1 |
| 15 | 156 | 1 |
| 16 | 190 | 1 |
| 17 | 230 | 1 |
| 18 | 276 | 1 |
| 19 | 322 | 1 |
| 20 | <377 | ? |
For this hypergraph we also considered the 2-colourable turan problem, i.e.
the maximum number of edges in a 2-colourable hypergraph without H as a
subgraph.
The Turan hypergraphs.
| N | ex(H,N) | Number of Turan graphs |
| 7 | 14 | 3 |
| 8 | 21 | 4 |
| 9 | 30 | 9 |
| 10 | 42 | 2 |
| 11 | 56 | 3 |
| 12 | 73 | 1 |
| 13 | 93 | 1 |
| 14 | 116 | 7 |
| 15 | 144 | 1 |
| 16 | 174 | 7 |
| 17 | 209-210 | ? |