On graphic elementary lifts of graphic matroids

TL;DR

This paper characterizes when all lifted-graphic matroids derived from a graphic matroid remain graphic, using forbidden-minor characterization and the splitting operation, advancing understanding of matroid lift properties.

Contribution

It provides a forbidden-minor characterization for graphic matroids whose all lifted-graphic matroids are also graphic, using the splitting operation.

Findings

Identifies conditions for all lifted-graphic matroids to be graphic

Develops a forbidden-minor characterization

Uses the splitting operation to analyze matroid properties

Abstract

Zaslavsky introduced the concept of lifted-graphic matroid. For binary matroids, a binary elementary lift can be defined in terms of the splitting operation. In this paper, we give a method to get a forbidden-minor characterization for the class of graphic matroids whose all lifted-graphic matroids are also graphic using the splitting operation.