Document Type

Article

Publication Date

1-2017

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.

Repository Citation

Neudauer, N. A., & Slilaty, D. (2017). Bounding and Stabilizing Realizations of Biased Graphs With a Fixed Group. Journal of Combinatorial Theory, Series B, 122, 149-166.
https://corescholar.libraries.wright.edu/math/311