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A characterization of projective-planar signed graphs |
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| Authors: | Dan Archdeacon Marisa Debowsky |
| Institution: | Department of Mathematics and Statistics, University of Vermont, 16 Colchester Avenue, Burlington, VT 05405, USA |
| Abstract: | A signed graph has a plus or minus sign on each edge. A simple cycle is positive or negative depending on whether it contains an even or odd number of negative edges, respectively. We consider embeddings of a signed graph in the projective plane for which a simple cycle is essential if and only if it is negative. We characterize those signed graphs that have such a projective-planar embedding. Our characterization is in terms of a related signed graph formed by considering the theta subgraphs in the given graph. |
| Keywords: | Signed graphs Projective plane Kuratowski |
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