Downlinking $(K_v,\Gamma)$designs to $P_3$designs
Abstract
Let G' be a subgraph of a graph G. We define a downlink 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 downlinks in general and prove that any (K_v,G)design might be downlinked 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 downlink to a design of order at most v+3. This bound is then improved for several classes of graphs Gamma, by providing explicit constructions.
 Publication:

arXiv eprints
 Pub Date:
 April 2010
 arXiv:
 arXiv:1004.4127
 Bibcode:
 2010arXiv1004.4127B
 Keywords:

 Mathematics  Combinatorics;
 05C51;
 05B30;
 05C38
 EPrint:
 19 Pages