Cobiased graphs: Single-element extensions and elementary quotients of graphic matroids

2024/01/31 by Daniel Slilaty, Slilaty, Daniel, Thomas Zasĺavsky +1
Computer Science · #05B35 (Primary) 05C22 (Secondary) #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #Digital Image Processing Techniques #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2401.17616

openalex publication_date 2024/01/31 · openalex created_date 2024/02/02 · openalex updated_date 2026/07/28

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, dual graphical structure that we call a cobiased graph and use it to characterize single-element extensions and elementary quotients of graphic matroids.

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