The α-Arboricity of Complete Uniform Hypergraphs
نویسندگان
چکیده
منابع مشابه
The α-Arboricity of Complete Uniform Hypergraphs
α-acyclicity is an important notion in database theory. The α-arboricity of a hypergraphH is the minimum number of α-acyclic hypergraphs that partition the edge set of H. The α-arboricity of the complete 3-uniform hypergraph is determined completely.
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Using a generalisation of Hamiltonian cycles to uniform hypergraphs due to Katona and Kierstead, we define a new notion of a Hamiltonian decomposition of a uniform hypergraph. We then consider the problem of constructing such decompositions for complete uniform hypergraphs, and describe its relationship with other topics, such as design theory.
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By K n we denote the complete k-uniform hypergraph of order n, 1 6 k 6 n−1, i.e. the hypergraph with the set Vn = {1, 2, ..., n} of vertices and the set ( Vn k ) of edges. If there exists a permutation σ of the set Vn such that {E, σ(E), ..., σq−1(E)} is a partition of the set ( Vn k ) then we call it cyclic q-partition of K n and σ is said to be a (q, k)-complementing. In the paper, for arbitr...
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A k−uniform hypergraphH is a pair (V, ε), where V = {v1, v2, . . . , vn} is a set of n vertices and ε is a family of k-subset of V called hyperedges. A cycle of length l of H is a sequence of the form (v1, e1, v2, e2, . . . , vl, el, v1), where v1, v2, . . . , vl are distinct vertices, and e1, e2, . . . , el are k-edges of H and vi, vi+1 ∈ ei, 1 ≤ i ≤ l, where addition on the subscripts is modu...
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We consider the problem of covering the complete r-uniform hypergraphs on n vertices using complete r-partite graphs. We obtain lower bounds on the size of such a covering. For small values of r our result implies a lower bound of Ω( e r r √ r n log n) on the size of any such covering. This improves the previous bound of Ω(rn log n) due to Snir [5]. We also obtain good lower bounds on the size ...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2011
ISSN: 0895-4801,1095-7146
DOI: 10.1137/100806035