Hypergraphs with independent neighborhoods
نویسندگان
چکیده
For each k ≥ 2, let ρk ∈ (0, 1) be the largest number such that there exist k-uniform hypergraphs on n vertices with independent neighborhoods and (ρk + o(1)) ( n k ) edges as n → ∞. We prove that ρk = 1 − 2 log k/k + Θ(log log k/k) as k → ∞. This disproves a conjecture of Füredi and the last two authors.
منابع مشابه
The independent neighborhoods process
A triangle T (r) in an r-uniform hypergraph is a set of r + 1 edges such that r of them share a common (r − 1)-set of vertices and the last edge contains the remaining vertex from each of the first r edges. Our main result is that the random greedy triangle-free process on n points terminates in an r-uniform hypergraph with independence number O((n log n)). As a consequence, using recent result...
متن کاملno-homomorphism conditions for hypergraphs
In this paper, we define some new homomorphism-monotone parameters for hypergraphs. Using these parameters, we extend some graph homomorphism results to hypergraph case. Also, we present some bounds for some well-known invariants of hypergraphs such as fractional chromatic number,independent numer and some other invariants of hyergraphs, in terms of these parameters.
متن کاملAlmost all triple systems with independent neighborhoods are semi-bipartite
The neighborhood of a pair of vertices u, v in a triple system is the set of vertices w such that uvw is an edge. A triple system H is semi-bipartite if its vertex set contains a vertex subset X such that every edge of H intersects X in exactly two points. It is easy to see that if H is semi-bipartite, then the neighborhood of every pair of vertices in H is an independent set. We show a partial...
متن کاملSemantic Neighborhoods as Hypergraphs
Ambiguity preserving representations such as lattices are very useful in a number of NLP tasks, including paraphrase generation, paraphrase recognition, and machine translation evaluation. Lattices compactly represent lexical variation, but word order variation leads to a combinatorial explosion of states. We advocate hypergraphs as compact representations for sets of utterances describing the ...
متن کاملShort paths in 3-uniform quasi-random hypergraphs
Frankl and Rödl [3] proved a strong regularity lemma for 3-uniform hypergraphs, based on the concept of δ-regularity with respect to an underlying 3-partite graph. In applications of that lemma it is often important to be able to “glue” together separate pieces of the desired subhypergraph. With this goal in mind, in this paper it is proved that every pair of typical edges of the underlying gra...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Combinatorica
دوره 30 شماره
صفحات -
تاریخ انتشار 2010