The independent neighborhoods process
نویسندگان
چکیده
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...
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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.
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A 4-graph is odd if its vertex set can be partitioned into two sets so that every edge intersects both parts in an odd number of points. Let b(n) = max α { α ( n− α 3 ) + (n− α) ( α 3 )} = ( 1 2 + o(1) )( n 4 ) denote the maximum number of edges in an n-vertex odd 4-graph. Let n be sufficiently large, and let G be an n-vertex 4-graph such that for every triple xyz of vertices, the neighborhood ...
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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...
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ژورنال
عنوان ژورنال: Israel Journal of Mathematics
سال: 2016
ISSN: 0021-2172,1565-8511
DOI: 10.1007/s11856-016-1331-8