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Abstract

We explore the work of Evans et al., who in turn have built on Schnyder’s definition of the dimension of a graph, and extended Schnyder woods to higher dimensions. Here we discuss d-realizers: sequences of d permutations on a set of vertices required to have empty intersection and d ‘suspension’ vertices. We will present a minimal graph having no d-realizer, and numerous graphs on 5, 6 and 7 vertices that do have one. Finally, we consider what possible characterization of graphs having a d-realizer could extend the triangulated-graph characterization found by Schnyder for 3 dimensional graphs.