On decompositions of complete $k$-uniform hypergraphs
نویسندگان
چکیده
منابع مشابه
Hamiltonian decompositions of complete k-uniform hypergraphs
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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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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Let m ≥ 2 and k ≥ 2 be integers. We show that K k×m has a decomposition into Hamilton cycles of Kierstead-Katona type if k | m. We also show that K (3) 3×m − T has a decomposition into Hamilton cycles where T is a 1-factor if and only if 3 m and m = 4. We introduce a notion of symmetry and comment on the existence of symmetric Hamilton cycle decompositions of K (k) k×m.
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We study the minimum number of complete r-partite r-uniform hypergraphs needed to partition the edges of the complete r-uniform hypergraph on n vertices and we improve previous results of Alon.
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In this paper we consider the problem of determining all values of v for which there exists a decomposition of the complete 3-uniform hypergraph on v vertices into edge-disjoint copies of a given 3-uniform hypergraph. We solve the problem for each 3-uniform hypergraph having at most three edges and at most six vertices, and for the 3-uniform hypergraph of order 6 whose edges form the lines of t...
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ژورنال
عنوان ژورنال: Czechoslovak Mathematical Journal
سال: 1978
ISSN: 0011-4642,1572-9141
DOI: 10.21136/cmj.1978.101518