Combinatorics: set systems, hypergraphs, families of vectors, and combinatorial probability
Combinatorics: set systems, hypergraphs, families of vectors, and combinatorial probability
The maximum size of 3-uniform hypergraphs not containing a fano plane
Journal of Combinatorial Theory Series B
On the Turán number of triple systems
Journal of Combinatorial Theory Series A
Extremal Graph Theory
The Turán Number Of The Fano Plane
Combinatorica
On A Hypergraph Turán Problem Of Frankl
Combinatorica
On Triple Systems with Independent Neighbourhoods
Combinatorics, Probability and Computing
A hypergraph extension of Turán's theorem
Journal of Combinatorial Theory Series B
Journal of Combinatorial Theory Series A
Pairwise intersections and forbidden configurations
European Journal of Combinatorics - Special issue on extremal and probabilistic combinatorics
A new generalization of Mantel's theorem to k-graphs
Journal of Combinatorial Theory Series B
Combinatorics, Probability and Computing
The minimum size of 3-graphs without a 4-set spanning no or exactly three edges
European Journal of Combinatorics
Exact computation of the hypergraph Turán function for expanded complete 2-graphs
Journal of Combinatorial Theory Series B
Counting substructures II: Hypergraphs
Combinatorica
| Hi-index | 0.00 |
A cancellative hypergraph has no three edges A, B, C with AΔB ⊂ C. We give a new short proof of an old result of Bollobás, which states that the maximum size of a cancellative triple system is achieved by the balanced complete tripartite 3-graph. One of the two forbidden subhypergraphs in a cancellative 3-graph is F5 = {abc, abd, cde}. For n ≥ 33 we show that the maximum number of triples on n vertices containing no copy of F5 is also achieved by the balanced complete tripartite 3-graph. This strengthens a theorem of Frankl and Füredi, who proved it for n ≥ 3000. For both extremal results, we show that a 3-graph with almost as many edges as the extremal example is approximately tripartite. These stability theorems are analogous to the Simonovits stability theorem for graphs.