Enclosings of a-fold triple systems

Abstract

Over the past five years, Hurd et al considered the problem of enclosing a triple system TS(v, λ) into a triple system TS(v+s, λ+m), focusing on smallest possible enclosings. In this paper, their result is generalized using a new proof based on a graph-theoretic technique. Various constructions are presented; they are exhaustive in the sense that, for each possible congruence of the parameters v or s and m, at least one construction can be applied to obtain an enclosing. In each construction, the value of v or s is restricted.