Summary: Gray Code Enumeration of Plane Straight­Line Graphs #
O. Aichholzer + F. Aurenhammer # C. Huemer § B. Vogtenhuber ¶
Abstract
We develop Gray code enumeration schemes for ge­
ometric graphs in the plane. The considered graph
classes include plane straight­line graphs, plane span­
ning trees, and connected plane straight­line graphs.
Previous results were restricted to the case where the
underlying vertex set is in convex position.
1 Introduction
Let E = {e 1 , . . . , e m } be an ordered set. For the pur­
poses of this paper, E will consist of the m = # n
2 # line
segments spanned by a set S of n points in the plane,
in lexicographical order. Consider a collection A of
subsets of E. For instance, think of A being the class
of all crossing­free spanning trees of S. We associate
each member A i # A with its containment vector b i
with respect to E. That is, b i is a binary string of
length m whose j th bit is 1 if e j # A i and 0, other­

Source: Aurenhammer, Franz - Institute for Theoretical Computer Science, Technische Universität Graz

Collections: Computer Technologies and Information Sciences