The genus 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 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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A hypergraph H on n nodes is complete 3-uniform if the hyperedges are precisely the set of all node triples. A one-factor of H is a set of hyperedges that cover each node exactly once. According to Baranyai's proof, the hyperedges of H can be partitioned into one-factors iff n ≡ 0 (mod 3). Though the proof is constructive, it leads to an O(2)-time algorithm. We investigate a method for computin...
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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.
متن کاملDecomposing complete 3-uniform hypergraphs into Hamiltonian cycles
Using the Katona-Kierstead definition of a Hamiltonian cycle in a uniform hypergraph, we continue the investigation of the existence of a decomposition of the complete 3-uniform hypergraph into Hamiltonian cycles began by Bailey and Stevens. We also discuss two extensions of the problem: to the complete 3-uniform hypergraph from which a parallel class of triples has been removed, and to the com...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 2020
ISSN: 0095-8956
DOI: 10.1016/j.jctb.2019.08.002