then G(n ; l) contains k independent edges . It is easy to see that the above result is best possible since the complete graph of 2k-1 vertices and the graph of vertices x1, . . ., xk-1 ; Yl, • • •, Yn-k+l and edges (x1 , xj), 1I ; (x1 , y), 1 i :!-< k 1, 1-yj :!5 n k + 1 clearly does not contain k independent edges . By an r-graph o(r) we shall mean a graph whose basic elements are its vertices and r-tuples ; for r = 2 we obtain the ordinary graphs . G (r) (n ; m) will denote an r-graph of n… Expand

GIVEN a set X and a natural number r denote by X(r) the set of relement subsets of X. An r-graph or hypergraph G is a pair (V, T), where V is a finite set and T c V(r) . We call v E V a vertex of G… Expand

The intensive use of the delta-system method is used to determine exk(n, Pℓ(k) exactly for all fixed ℓ ≥1, k≥4, and sufficiently large n, and describe the unique extremal family.Expand

Ex(n, F_m) is determined for all integers $n$ with minor conditions, which extends their partial results and partly confirm the conjecture proposed by Bushaw and Kettle for $ex( n, k\cdot P_l)$.Expand

Let f(n, r, k) be the minimal number such that every hypergraph larger than f(n, r, k) contained in ([n] r ) contains a matching of size k, and let g(n, r, k) be the minimal number such that every… Expand

Let n, s, k be three positive integers such that 1 ≤ s ≤ (n − k + 1)/k and let [n] = {1, . . . , n}. Let H be a k-graph with vertex set [n], and let e(H) denote the number of edges of H . Let ν(H)… Expand

2. Notation The letters a, b, c, d, x, y, z denote finite sets of non-negative integers, all other lower-case letters denote non-negative integers. If fc I, then [k, I) denotes the set… Expand