Counting Connected Hypergraphs via the Probabilistic Method
نویسندگان
چکیده
منابع مشابه
Counting Connected Graphs and Hypergraphs via the Probabilistic Method
It is exponentially unlikely that a sparse random graph or hypergraph is connected, but such graphs occur commonly as the giant components of larger random graphs. This simple observation allows us to estimate the number of connected graphs, and more generally the number of connected d-uniform hypergraphs, on n vertices with m = O(n) edges. We also estimate the probability that a binomial rando...
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We develop a theory of regularity inheritance in 3-uniform hypergraphs. As a simple consequence we deduce a strengthening of a counting lemma of Frankl and Rödl. We believe that the approach is sufficiently flexible and general to permit extensions of our results in the direction of a hypergraph blow-up lemma.
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We develop a theory of regularity inheritance in 3-uniform hypergraphs. As a simple consequence we deduce a strengthening of a counting lemma of Frankl and Rödl. We believe that the approach is sufficiently flexible and general to permit extensions of our results in the direction of a hypergraph blow-up lemma.
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ژورنال
عنوان ژورنال: Combinatorics, Probability and Computing
سال: 2016
ISSN: 0963-5483,1469-2163
DOI: 10.1017/s0963548315000309