1. Intrinsically linked signed graphs in projective space
- Author
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Duong, Yen, Foisy, Joel, Meehan, Killian, Merrill, Leanne, and Snyder, Lynea
- Subjects
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GRAPH theory , *PROJECTIVE spaces , *EMBEDDINGS (Mathematics) , *COMBINATORICS , *MATHEMATICAL analysis , *COMBINATORIAL set theory - Abstract
Abstract: We define a signed embedding of a signed graph into real projective space to be an embedding such that an embedded cycle is 0-homologous if and only if it is balanced. We characterize signed graphs that have a linkless signed embedding. In particular, we exhibit 46 graphs that form the complete minor-minimal set of signed graphs that contain a non-split link for every signed embedding. With one trivial exception, these graphs are derived from different signings of the seven Petersen family graphs. [Copyright &y& Elsevier]
- Published
- 2012
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