Let H be a subgraph of G. An H-design (V, C) of order nu and index mu is embedded into a G-design (X, B) of order nu + omega and index lambda if mu <= lambda, V subset of X and there is an injective mapping f : C -> B such that B is subgraph of f(B) for every B is an element of C. For every pair of positive integers nu, lambda, (except when lambda = 3 and nu = 30, 34, 42, 46, 54, 58, 66 or lambda = 5 and nu = 19) we determine the minimum value of omega such that there exists a balanced incomplete block design of order nu + omega, index lambda and block-size 4 which embeds a P(4)-design of order nu and index mu = 1 (P(4) denotes the path of length 3). (C) 2009 Published by Elsevier B.V.
|Titolo:||Minimum embedding of a P(4)-design into a balanced incomplete block design of index lambda|
|Data di pubblicazione:||2009|
|Appare nelle tipologie:||1.1 Articolo in rivista|