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arXiv · 2401.17616

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

Daniel Slilaty·Thomas Zaslavsky
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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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Daniel Slilaty, Thomas Zaslavsky. 2024-01-31. Cobiased graphs: Single-element extensions and elementary quotients of graphic matroids. https://arxiv.org/abs/2401.17616

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