Intrinsically linked signed graphs in projective space

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 mino...

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Bibliographic Details
Published in:Discrete mathematics 2012-07, Vol.312 (12-13), p.2009-2022
Main Authors: Duong, Yen, Foisy, Joel, Meehan, Killian, Merrill, Leanne, Snyder, Lynea
Format: Article
Language:English
Subjects:
Balancing
Graphs
Intrinsically linked
Links
Mathematical analysis
Projective space
Signed graph
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Summary: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.
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2012.03.025