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Article
Bounding and Stabilizing Realizations of Biased Graphs With a Fixed Group
Journal of Combinatorial Theory, Series B
Document Type
Article
Publication Date
1-1-2017
Disciplines
Abstract
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 to Whittle’s Stabilizer Theorem for Γ-realizations of biased graphs.
DOI
10.1016/j.jctb.2016.05.008
Citation Information
Nancy Ann Neudauer and Dan Slilaty. "Bounding and Stabilizing Realizations of Biased Graphs With a Fixed Group" Journal of Combinatorial Theory, Series B Vol. 122 (2017) p. 149 - 166 ISSN: 0095-8956 Available at: http://works.bepress.com/dan_slilaty/12/