Graphic Elementary Lift of Cographic Matroids
Shital D. Solanki, Ganesh Mundhe, S. B. Dhotre

TL;DR
This paper investigates the conditions under which elementary lifts of cographic matroids result in graphic matroids, contributing to the understanding of matroid transformations and their properties.
Contribution
It characterizes cographic matroids whose elementary lifts are graphic, advancing the theory of matroid lifts and their structural implications.
Findings
Identifies conditions for elementary lifts of cographic matroids to be graphic
Provides characterization of cographic matroids with graphic elementary lifts
Enhances understanding of matroid lift operations and their effects
Abstract
A matroid is a lift of a binary matroid , if when for some binary matroid and and is called an elementary lift of , if . A splitting operation on a binary matroid can result in an elementary lift. An elementary lift of a cographic or a graphic matroid need not be cographic or graphic. We intend to characterize the cographic matroids whose elementary lift is a graphic matroid.
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Taxonomy
TopicsAdvanced Graph Theory Research
