Given an hypergraph H(3), uniform of rank 3, an H(3)-decomposition of the complete hypergraph K(3):_v is a collection of hypergraphs, all isomorphic to H(3), whose edge-sets partition the edge-set of K(3)_v . An H(3)-decomposition of K(3)_v is also called an H(3)-design. In every decomposition, the hypergraphs of the partition are said to be the blocks of the system. Every decomposition is said to be balanced if the number of blocks containing any given vertex is a constant. In this paper, we give some construction for P(3)(1, 5)-designs, balanced P(3)(1, 5)-designs, P(3)(2, 4)-designs, balanced P(3)(2, 4)- designs, all systems which we will say to belong to the class of the hyperpath-designs.
Some techniques for the construction of hyperpath-designs - a survey
LO FARO, GiovanniSecondo
;
2017-01-01
Abstract
Given an hypergraph H(3), uniform of rank 3, an H(3)-decomposition of the complete hypergraph K(3):_v is a collection of hypergraphs, all isomorphic to H(3), whose edge-sets partition the edge-set of K(3)_v . An H(3)-decomposition of K(3)_v is also called an H(3)-design. In every decomposition, the hypergraphs of the partition are said to be the blocks of the system. Every decomposition is said to be balanced if the number of blocks containing any given vertex is a constant. In this paper, we give some construction for P(3)(1, 5)-designs, balanced P(3)(1, 5)-designs, P(3)(2, 4)-designs, balanced P(3)(2, 4)- designs, all systems which we will say to belong to the class of the hyperpath-designs.File | Dimensione | Formato | |
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