Hypercycle Systems of 5-Cycles in Complete 3-Uniform Hypergraphs
نویسندگان
چکیده
In this paper, we consider the problem of constructing hypercycle systems 5-cycles in complete 3-uniform hypergraphs. A system C(r,k,v) order v is a collection r-uniform k-cycles on v-element vertex set, such that each r-element subset an edge precisely one those k-cycles. We present cyclic C(3,5,v) orders v=25,26,31,35,37,41,46,47,55,56, highly symmetric construction for v=40, and 2-split constructions 32,40,50,52. As consequence, all v≤60 permitted by divisibility conditions admit system. New recursive are also introduced.
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ژورنال
عنوان ژورنال: Mathematics
سال: 2021
ISSN: ['2227-7390']
DOI: https://doi.org/10.3390/math9050484