 
Summary: Gray Code Enumeration of Plane StraightLine Graphs #
O. Aichholzer 1 , F. Aurenhammer 2 , C. Huemer 3 , B. Vogtenhuber 1
1 Institute for Software Technology, University of Technology, Graz, Austria
2 Institute for Theoretical Computer Science, University of Technology, Graz, Austria
3 Departament de Matematica Aplicada, Universitat Politecnica de Catalunya, Barcelona, Spain
Abstract. We develop Gray code enumeration schemes for geometric straightline graphs in the plane.
The considered graph classes include plane graphs, connected plane graphs, and plane spanning trees.
Previous results were restricted to the case where the underlying vertex set is in convex position.
Key words. Geometric graphs, enumeration scheme, Gray codes
1. Introduction
Let E = {e 1 , . . . , e m } be an ordered set. For the purposes 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 plane
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,
otherwise. A (combinatorial) Gray code for the class A is an ordering A 1 , . . . , A t of A such
that b i+1 differs from b i by a transposition, for i = 1, . . . , t  1. For example (and as one of
the results of this paper), for plane spanning trees a Gray code exists such that successive trees
differ by a single edge move. Depending on the class we will consider, a transposition will be
