Embedding of E2-designs into 4-cycle systems

Abstract

A 4-cycle system C(υ, 4, λ) of order υ and index λ embeds an E₂-design on u points, u ≤ υ, if there is a subset of u points on which the 4-cycles induce the blocks of an E₂-design. In this paper it is settled the embedding of an E₂-design of order u into a C(υ, 4, λ).