 
Summary: Characterizing Planarity
Using Theta Graphs
Dan Archdeacon
Dept. of Math. and Stat.
University of Vermont
Burlington, VT, USA 05405
email: dan.archdeacon@uvm.edu
Jozef ź Sir'aźn
Department of Mathematics
Faculty of Civil Engineering Slovak Technical University
813 68 Bratislava, Slovakia
email: siran@lux.svf.stuba.sk
September 14, 1997
Abstract
A theta graph is a homeomorph of K 2;3 . In an embedded planar
graph the local rotation at one degreethree vertex of a theta graph
determines the local rotation at the other degreethree vertex. Using
this observation, we give a characterization of planar graphs in terms
of balance in an associated signed graph whose vertices are K 1;3 sub
graphs and whose edges correspond to theta graphs.
