Cobiased Graphs: Single-Element Extensions and Elementary Quotients of Graphic Matroids

Abstract

Zaslavsky (1991) introduced a graphical structure called a biased graph and used it to characterize all single-element coextensions and elementary lifts of graphic matroids. We introduce a new graphical structure that we call a cobiased graph and use it to characterize single-element extensions and elementary quotients of graphic matroids.