منابع مشابه
Daisies and Other Turán Problems
Our aim in this note is to make some conjectures about extremal densities of daisy-free families, where a ‘daisy’ is a certain hypergraph. These questions turn out to be related to some Turán problems in the hypercube, but they are also natural in their own right. We start by giving the daisy conjectures, and some related problems, and shall then go on to describe the connection with vertex-Tur...
متن کاملRainbow Turán Problems
For a fixed graph H, we define the rainbow Turán number ex∗(n,H) to be the maximum number of edges in a graph on n vertices that has a proper edge-colouring with no rainbow H. Recall that the (ordinary) Turán number ex(n,H) is the maximum number of edges in a graph on n vertices that does not contain a copy of H. For any non-bipartite H we show that ex∗(n,H) = (1+o(1))ex(n,H), and if H is colou...
متن کاملSupersaturation For Ramsey-Turán Problems
For an l-graph G, the Turán number ex(n,G) is the maximum number of edges in an n-vertex l-graph H containing no copy of G. The limit π(G) = limn→∞ ex (n,G)/ ( n l ) is known to exist [8]. The Ramsey-Turán density ρ(G) is defined similarly to π(G) except that we restrict to only those H with independence number o(n). A result of Erdős and Sós [3] states that π(G) = ρ(G) as long as for every edg...
متن کاملTurán Problems for Bipartite Graphs ∗
We consider an infinite version of the bipartite Turán problem. Let G be an infinite graph with V (G) = N, and let Gn be the n-vertex subgraph of G induced by the vertices {1, 2, . . . , n}. We show that if G is K2,t+1-free, then for infinitely many n, e(Gn) ≤ 0.471 √ tn3/2. Using the K2,t+1-free graphs constructed by Füredi, we construct an infinite K2,t+1-free graph with e(Gn) ≥ 0.23 √ tn3/2 ...
متن کاملNon-uniform Turán-type problems
Given positive integers n, k, t, with 2 ≤ k ≤ n, and t < 2, let m(n, k, t) be the minimum size of a family F of (nonempty distinct) subsets of [n] such that every k-subset of [n] contains at least t members of F , and every (k − 1)-subset of [n] contains at most t− 1 members of F . For fixed k and t, we determine the order of magnitude of m(n, k, t). We also consider related Turán numbers T≥r(n...
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ژورنال
عنوان ژورنال: Combinatorics, Probability and Computing
سال: 2011
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548311000319