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Discrete Mathematics
Article
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Discrete Mathematics
Article . 1993
License: Elsevier Non-Commercial
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Discrete Mathematics
Article . 1993 . Peer-reviewed
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The projective-planar signed graphs

Authors: Thomas Zaslavsky;

The projective-planar signed graphs

Abstract

A signature on a graph is an assignment of a plus or minus sign on each edge. A polygon in a signed graph is plus or minus depending on whether the number of edges with a minus sign is even or odd. An embedding of a signed graph embeds the underlying graph on some surface such that the minus polygons are precisely the orientation-reversing ones. In particular, if a signed graph is embedded in the projective plane, then the plus polygons are precisely the contractible ones. The author describes which signed graphs embed in the real projective plane by giving a list of six forbidden link minors (a link minor is a slight variation of a minor in which only links may be contracted). The six minors are based on the two Kuratowski graphs, \(K_ 5\) and \(K_{3,3}\). The author also gives a similar characterization in terms of eight forbidden topological subgraphs.

Keywords

forbidden topological subgraphs, link minors, Kuratowski graphs, Planar graphs; geometric and topological aspects of graph theory, Theoretical Computer Science, signed graph, polygon, embedding, surface, Discrete Mathematics and Combinatorics, Structural characterization of families of graphs, projective plane

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
10
Average
Top 10%
Average
hybrid