Hamilton decompositions of complete 3-uniform hypergraphs
نویسندگان
چکیده
منابع مشابه
Hamilton decompositions of complete 3-uniform hypergraphs
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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In 1973 Bermond, Germa, Heydemann and Sotteau conjectured that if n divides ( n k ) , then the complete k-uniform hypergraph on n vertices has a decomposition into Hamilton Berge cycles. Here a Berge cycle consists of an alternating sequence v1, e1, v2, . . . , vn, en of distinct vertices vi and distinct edges ei so that each ei contains vi and vi+1. So the divisibility condition is clearly nec...
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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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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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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1994
ISSN: 0012-365X
DOI: 10.1016/0012-365x(92)00572-9