Down-linking $(K_v,Γ)$-designs to $P_3$-designs

Details Down-linking $(K_v,Γ)$-designs to $P_3$-designs Down-linking $(K_v,Γ)$-designs to $P_3$-designs

2010-04-23

arxiv.org/abs/1004.4127v3

Mathematics

Combinatorics

19 Pages; corrected typos; final version

Scientific paper

Let G' be a subgraph of a graph G. We define a down-link from a (K_v,G)-design B to a (K_n,G')-design B' as a map f:B->B' mapping any block of B into one of its subgraphs. This is a new concept, closely related with both the notion of metamorphosis and that of embedding. In the present paper we study down-links in general and prove that any (K_v,G)-design might be down-linked to a (K_n,G')-design, provided that n is admissible and large enough. We also show that if G'=P_3, it is always possible to find a down-link to a design of order at most v+3. This bound is then improved for several classes of graphs Gamma, by providing explicit constructions.

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