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Full-Text Articles in Physical Sciences and Mathematics
Flexibility Of Projective-Planar Embeddings, John Maharry, Neil Robertson, Vaidy Sivaraman, Dan Slilaty
Flexibility Of Projective-Planar Embeddings, John Maharry, Neil Robertson, Vaidy Sivaraman, Dan Slilaty
Mathematics and Statistics Faculty Publications
Given two embeddings σ1 and σ2 of a labeled nonplanar graph in the projective plane, we give a collection of maneuvers on projective-planar embeddings that can be used to take σ1 to σ2
Bounding And Stabilizing Realizations Of Biased Graphs With A Fixed Group, Nancy Ann Neudauer, Dan Slilaty
Bounding And Stabilizing Realizations Of Biased Graphs With A Fixed Group, Nancy Ann Neudauer, Dan Slilaty
Mathematics and Statistics Faculty Publications
Given a group Γ and a biased graph (G, B), we define a what is meant by a Γ-realization of (G, B) and a notion of equivalence of Γ-realizations. We prove that for a finite group Γ and t ≥ 3, that there are numbers n(Γ) and n(Γ, t) such that the number of Γ-realizations of a vertically 3-connected biased graph is at most n(Γ) and that the number of Γ-realizations of a nonseparable biased graph without a (2Ct , ∅)-minor is at most n(Γ, t). Other results pertaining to contrabalanced biased graphs are presented as well as an analogue …