Characterizing planarity using theta graphs |
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| Authors: | Dan Archdeacon Josef Šráň |
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| Affiliation: | 1. Department of Mathematics and Statistics, University of Vermont, Burlington, VT, USA 05405;2. Department of Mathematics, Faculty of Civil Engineering, Slovak Technical University, 813 68 Bratislava, Slovakia |
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| Abstract: | A theta graph is a homeomorph of K2,3. In an embedded planar graph the local rotation at one degree-three vertex of a theta graph determines the local rotation at the other degree-three vertex. Using this observation, we give a characterization of planar graphs in terms of balance in an associated signed graph whose vertices are K1,3 subgraphs and whose edges correspond to theta graphs. © 1998 John Wiley & Sons, Inc. J Graph Theory 27: 17–20, 1998 |
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| Keywords: | planar graphs Kuratowski signed graphs |
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