منابع مشابه
Enumeration of Connected Uniform Hypergraphs
In this paper, we are concerned in counting exactly and asymptotically connected labeled b-uniform hypergraphs (b ≥ 3). Enumerative results on connected graphs are generalized here to connected uniform hypergraphs. For this purpose, these structures are counted according to the number of vertices and hyperedges. First, we show how to compute step by step the associated exponential generating fu...
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We consider the enumeration of unlabeled directed hypergraphs by using Pólya’s counting theory and Burnside’s counting lemma. Instead of characterizing the cycle index of the permutation group acting on the hyperarc set A, we treat each cycle in the disjoint cycle decomposition of a permutation ρ acting on A as an equivalence class (or orbit) of A under the operation of the group generated by ρ...
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A hypergraph is simple if it has no loops and no repeated edges, and a hypergraph is linear if it is simple and each pair of edges intersects in at most one vertex. For n ≥ 3, let r = r(n) ≥ 3 be an integer and let k = (k1, . . . , kn) be a vector of nonnegative integers, where each kj = kj(n) may depend on n. Let M = M(n) = ∑n j=1 kj for all n ≥ 3, and define the set I = {n ≥ 3 | r(n) divides ...
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Let r ≥ 2 be a fixed integer. For infinitely many n, let k = (k1, . . . , kn) be a vector of nonnegative integers such that their sum M is divisible by r. We present an asymptotic enumeration formula for simple r-uniform hypergraphs with degree sequence k. (Here “simple” means that all edges are distinct and no edge contains a repeated vertex.) Our formula holds whenever the maximum degree kmax...
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Finding the optimal execution order of join operations is a crucial task of today’s cost-based query optimizers. There are two approaches to identify the best plan: bottom-up and top-down join enumeration. But only the top-down approach allows for branchand-bound pruning, which can improve compile time by several orders of magnitude while still preserving optimality. For both optimization strat...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1983
ISSN: 0012-365X
DOI: 10.1016/0012-365x(83)90040-7