We study the problem of realizing a given graph as an -complex of a set of points in the plane. We study the realizability problem for trees and 2-trees. In the case of 2-trees, we confine our attention to the realizability of graphs as the
-complex minus faces of dimension two; in other words, realizability of the graph in terms of the 1-skeleton of the
-complex of the point set. We obtain both positive (realizability) and negative (non-realizability) results.
By: David Bremner; Jonathan Lenchner; Giuseppe Liotta; Christophe Paul; Marc Pouget; Svetlana Stolpner; Stephen Wismath
Published in: RC24605 in 2008
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