Maximum embedding of a E 2 (v − w, 4, 1) into a P(v, 4, λ)

Abstract

A path design P(v, 4, λ) of order v and index λ embeds a E 2-design E 2(u, 4, 1) on u points, u ≤ v, if there is a subset of u points on which the paths with 3 edges induce the blocks of a E 2-design. In this paper we determine, for every pair of positive integers v, λ, the minimum value of w such that there exists a P(v, 4, λ) which embeds a E 2(v − w, 4, 1).