Down-linking (K-nu, Gamma)-designs to P-3-designs

作者：Benini A^*; Giuzzi L; Pasotti A

来源：Utilitas Mathematica, 2013, 90: 3-21.

• down-link
• metamorphosis
• embedding
• (K-nu, Gamma)-design

Let Gamma%26apos; be a subgraph of a graph Gamma. We define a down-link from a (K-nu, Gamma)-design B to a (K-n, Gamma%26apos;)-design B%26apos; as a map f : B -%26gt; B%26apos; 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-nu, Gamma)-design might be down-linked to a (K-n, Gamma)-design, provided that n is admissible and large enough. We also show that if Gamma%26apos; = P-3 it is always possible to find a down-link to a design of order at most nu + 3. This bound is then improved for several classes of graphs Gamma, by providing explicit constructions.

• 出版日期2013-3