Given a 3-uniform hypergraph H(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 and the hypergraphs of the partition are said to be the blocks. An H(3)-design is said to be balanced if the number of blocks containing any given vertex of K(3) v is a constant. In this paper, we determine completely, without exceptions, the spectrum of balanced P(3)(1; 5)-designs.
The spectrum of balanced P(3)(1; 5)-designs
Bonacini, Paola;DI GIOVANNI, MARIA;Gionfriddo, Mario;Marino, Lucia;
2017-01-01
Abstract
Given a 3-uniform hypergraph H(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 and the hypergraphs of the partition are said to be the blocks. An H(3)-design is said to be balanced if the number of blocks containing any given vertex of K(3) v is a constant. In this paper, we determine completely, without exceptions, the spectrum of balanced P(3)(1; 5)-designs.File in questo prodotto:
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