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Projective-planar signed graphs and tangled signed graphs
  • Daniel C. Slilaty
  • Mathematics, Computer Science
  • J. Comb. Theory, Ser. B
  • 1 September 2007
A projective-planar signed graph has no two vertex-disjoint negative circles. We prove that every signed graph with no two vertex-disjoint negative circles and no balancing vertex is obtained byExpand
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On cographic matroids and signed-graphic matroids
We prove that a connected cographic matroid of a graph G is the bias matroid of a signed graph @S iff G imbeds in the projective plane. In the case that G is nonplanar, we also show that @S must beExpand
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Cellular automorphisms and self-duality
We catalog up to a type of reducibility all cellular automorphisms of the sphere, projective plane, torus, Klein bottle, and three-crosscaps (Dyck’s) surface. We also show how one can obtain allExpand
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Connectivity in frame matroids
We discuss the relationship between the vertical connectivity of a biased graph @W and the Tutte connectivity of the frame matroid of @W (also known as the bias matroid of @W).
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Algebraic Characterizations of Graph Imbeddability in Surfaces and Pseudosurfaces
Given a finite connected graph G and specifications for a closed, connected pseudosurface, we characterize when G can be imbedded in a closed, connected pseudosurface with the given specifications.Expand
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An algebraic characterization of projective-planar graphs
We give a detailed algebraic characterization of when a graph G can be imbedded in the projective plane. The characterization is in terms of the existence of a dual graph G on the same edge set as GExpand
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Decompositions of signed-graphic matroids
We give a decomposition theorem for signed graphs whose frame matroids are binary and a decomposition theorem for signed graphs whose frame matroids are quaternary.
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Bias matroids with unique graphical representations
Given a 3-connected biased graph @W with three node-disjoint unbalanced circles, at most one of which is a loop, we describe how the bias matroid of @W is uniquely represented by @W.
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Matroid Duality From Topological Duality In Surfaces Of Nonnegative Euler Characteristic
Let G be a connected graph that is 2-cell embedded in a surface S, and let G* be its topological dual graph. We will define and discuss several matroids whose element set is E(G), for S homeomorphicExpand
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The Regular Excluded Minors for Signed-Graphic Matroids
We show that the complete list of regular excluded minors for the class of signed-graphic matroids is M*(G1),. . . , M*(G29), R15, R16. Here G1,. . . , G29 are the vertically 2-connected excludedExpand
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