The Spectrum of P(h)(h-1,h+1)-Designs

Di Giovanni M, Castelli V and Gionfriddo M

Published on: 2019-09-05

Abstract

Given an hypergraph H(h), uniform of rank h, an H(h)-design [or also a design of type H(h)] of order v is a pair Σ = ( X,B ), where X is a  set of cardinality v and  is a collection of hypergraphs, all isomor- phic to H(h), such that every h-subset of X is an edge of exactly one hypergraph H(h) ∈ B. An hyperpath P2 (h) is an uniform hypergraph, having two edges which are not disjoint. In this paper we study the spectrum of hyperpath-designs of type P2(h), for any h, in the case of hyperedges have h − 1 vertices in common, and we determine it almost completely, with the exception of some particular cases.

Keywords

Hypergrahs; H-Designs

Introduction