Transversals and blocking sets in H(3)-designs

Valerio Castelli, Maria Di Giovanni, Mario Gionfriddo

Abstract


If H(h) is a subhypergraph of order  n of  Kv(h), the complete and h-uniform hypergraph of order v, an H(h)-decomposition of Kv(h), also called an H(h)-design of order v, is a pair Σ=(X,B), where B  is a partition of the  edge-set of Kv(h) into classes generating hypergraphs all isomorphic to H(h). The classes of the partition are said to be the blocks of Σ. Using hypergraph terminology, if Σ=(X,B) is an H(h)-design, a transversal T  of Σ is a subset of intersecting every block of Σ. The transversal number  of Σ is the minimum number τ(Σ)=τ for which there exists a transversal of Σ having cardinality τ.  A blocking set B  of Σ is a subset of such that both  and CX(B)  are transversals. In this paper, the existence of transversals and blocking sets in H(3)-designs are studied.

Keywords


Transversals; Blocking sets; Hypergraphs

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DOI: http://dx.doi.org/10.1478/AAPP.96S2A3

Copyright (c) 2018 Mario Gionfriddo, Maria Di Giovanni, Valerio Castelli

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