 
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
