Embedding a Restricted Class of Partial \(K_4\)-Designs

Abstract

Given a partial \(K_4\)-design \((X, {P})\), if \(x \in X\) is a vertex which occurs in exactly one block of \({P}\), then call \(x\) a free vertex. In this paper, a technique is described for obtaining a cubic embedding of any partial \(K_4\)-design with the property that every block in the partial design contains at least two free vertices.