• Corpus ID: 18659689

# A PROBLEM ON INDEPENDENT r-TUPLES

@inproceedings{Erdos1965APO,
title={A PROBLEM ON INDEPENDENT r-TUPLES},
author={Paul L. Erdos},
year={1965}
}
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…
156 Citations
SETS OF INDEPENDENT EDGES OF A HYPERGRAPH
• Mathematics
• 1976
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
Exact solution of the hypergraph Turán problem for k-uniform linear paths
• Mathematics
Comb.
• 2014
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.
Turán numbers for disjoint paths
• Mathematics
J. Graph Theory
• 2021
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 $ex( n, k\cdot P_l)$.
SIZE CONDITIONS FOR THE EXISTENCE OF RAINBOW MATCHINGS
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
Families with no matchings of size s
• Mathematics
Electron. Notes Discret. Math.
• 2017
Hypergraph Turán numbers of linear cycles
• Mathematics
J. Comb. Theory, Ser. A
• 2014
A stability result on matchings in 3-uniform hypergraphs
• Mathematics
• 2021
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)