More than forty years ago, Erdős conjectured that for any t ≤ nk , every k-uniform hypergraph on n vertices without t disjoint edges has at most max {( kt−1 k ) , ( n k ) − ( n−t+1 k )} edges. Although this appears to be a basic instance of the hypergraph Turán problem (with a t-edge matching as the excluded hypergraph), progress on this question has remained elusive. In this paper, we verify t...

This paper deals with approximations of maximum independent sets in non-uniform hypergraphs of low degree. We obtain the first performance ratio that is sublinear in terms of the maximum or average degree of the hypergraph. We extend this to the weighted case and give a O(D̄ log log D̄/ log D̄) bound, where D̄ is the average weighted degree in a hypergraph, matching the best bounds known for the sp...

A 2-packing of a hypergraph H is a permutation σ on V (H) such that if an edge e belongs to E(H), then σ(e) does not belong to E(H). We prove that a hypergraph which does not contain neither empty edge ∅ nor complete edge V (H) and has at most 12n edges is 2-packable. A 1-uniform hypergraph of order n with more than 1 2n edges shows that this result cannot be improved by increasing the size of H.

We consider edge colourings of K n – the complete r-uniform hypergraph on n vertices. Our main question is: how ‘colourful’ can such a colouring be if we restrict the number of colours locally? The local restriction is formulated as follows: for a fixed hypergraph H and an integer k we call a colouring (H, k)-local, if every copy of H in the complete hypergraph K n picks up at most k different ...

We present an algorithm that colors a random 2-colorable 3-uniform hypergraph optimally in expected running time O(n5 log n).

We give an upper bound on the sum of squares of ‘-degrees in a k-uniform hypergraph in terms of ‘; k and the number of vertices and edges of the hypergraph, where a ‘-degree is the number of edges of the hypergraph containing a 0xed ‘-element subset of the vertices. For ordinary graphs this bound coincides with one given by de Caen. We show that our bound implies the quadratic LYM-inequality fo...

A new hypergraph coloring problem is introduced by de ning N(H; e) as the maximal number of colors in a vertex coloring of a hypergraph H = (V; E) , which has not more than e di erent colors in every edge. Our main results concern the asymptotic behaviour of this quantity for the uniform hypergraph H(n; `; k) = (V(n; `); E(n; `; k)) with vertex set V(n; `) = ǹ for n = f1; 2; : : : ; ng and edge...

In this paper we show that every family of triples, that is, a 3-uniform hypergraph, with minimum degree at least ( 5− √ 5 3 +γ) (

We prove that a k-uniform self-complementary hypergraph of order n exists, if and only if ( n k ) is even.

We prove the generalized Ramsey-type result on large 2-coloured matchings in a 3-coloured complete 3-uniform hypergraph, supporting a conjecture by A. Gyárfás.