Edge orbits and cyclic and r-pyramidal decompositions of complete 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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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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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2018
ISSN: 0012-365X
DOI: 10.1016/j.disc.2018.08.018