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On independent sets in hypergraphs
TLDR
It is proved that if Hn is an n-vertex r+1-uniform hypergraph in which every r-element set is contained in at most d edges, where 0 0 satisfies cr~r/e as ri¾?∞, then cr improves and generalizes several earlier results and gives an application to hypergraph Ramsey numbers involving independent neighborhoods.
On the Turán Number of Triple Systems
  • D. Mubayi, V. Rödl
  • Computer Science, Mathematics
    J. Comb. Theory, Ser. A
  • 1 October 2002
TLDR
This work determines the Turan densities of several 3-graphs that were not previously known and gives a new proof of a result of Frankl and Furedi that π(H) =2/9, where H has edges 123,124, 345.
Rainbow Turán Problems
TLDR
The rainbow Turán problem for even cycles is studied, and the bound $\ex^*(n,C_6) = O(n^{4/3})$, which is of the correct order of magnitude, is proved.
Erdos-Ko-Rado for three sets
  • D. Mubayi
  • Computer Science, Mathematics
    J. Comb. Theory, Ser. A
  • 1 April 2006
TLDR
It is proved that |F| ≤ (n-1 k-1) with equality only when ∩F∈F ≠ , which settles a conjecture of Frankl and Furedi [2].
Stability theorems for cancellative hypergraphs
TLDR
For both extremal results, it is shown that a 3-graph with almost as many edges as the extremal example is approximately tripartite, and stability theorems are analogous to the Simonovits stability theorem for graphs.
Erdős–Ko–Rado in Random Hypergraphs
TLDR
It is proved that every non-trivial intersecting k-uniform hypergraph can be covered by k2 − k + 1 pairs, which is sharp as evidenced by projective planes, which improves upon a result of Sanders.
Set systems without a simplex or a cluster
TLDR
The following result is proved which simultaneously addresses an old conjecture of Chvátal and a recent conjecture of the second author and generalises a question of Erdős and a result of Milner, who proved the case d=2.
Turán problems and shadows I: Paths and cycles
TLDR
This work extends the work of Furedi, Jiang and Seiver who solved the problem of the maximum number of edges in an r-graph with n vertices not containing a given r- graph G and solves the case of ( k, r ) = ( 4, 3 ) , which needs a special treatment.
Proof Of A Conjecture Of Erdős On Triangles In Set-Systems
TLDR
The main result implies that for r ≥ 3 and n ≥ 3r/2, equality holds if and only if user1 A consists of all r-element subsets containing a fixed element.
Note – Edge-Coloring Cliques with Three Colors on All 4-Cliques
  • D. Mubayi
  • Mathematics, Computer Science
    Comb.
  • 1 February 1998
TLDR
is constructed such that every copy of has at least three colors on its edges, and improves upon the previous probabilistic bound of due to Erdős and Gyárfás.
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