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

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.
Balanced; Blocks; Hypergraphs decomposition; Discrete Mathematics and Combinatorics
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/315020
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