Orientations of Single-Element Extensions of Graphic Matroids

Dan Slilaty

doi:10.61091/jcmcc128-12

Orientations of Single-Element Extensions of Graphic Matroids

Dan Slilaty

Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

Slilaty and Zaslavsky (2024) characterized all single-element extensions of graphic matroids in terms of a graphical structure called a cobiased graph. In this paper we characterize all orientations of a single-element extension of a graphic matroid in terms of graphically dened orientations of its associated cobiased graph. We also explain how these orientations can be canonically understood as dual to orientations of biased graphs if and only if the underlying graph is planar.

Original language	American English
Pages (from-to)	199-213
Journal	Journal of Combinatorial Mathematics and Combinatorial Computing
Volume	128
DOIs	https://doi.org/10.61091/jcmcc128-12
State	Published - 2026

Keywords

Cobiased graph
single-element extension
Orientation
Duality

Disciplines

Mathematics

Access to Document

10.61091/jcmcc128-12License: CC BY

orientations-of-single-element-extensions-of-graphic-matroidsFinal published version, 866 KBLicense: CC BY

Cite this

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abstract = "Slilaty and Zaslavsky (2024) characterized all single-element extensions of graphic matroids in terms of a graphical structure called a cobiased graph. In this paper we characterize all orientations of a single-element extension of a graphic matroid in terms of graphically dened orientations of its associated cobiased graph. We also explain how these orientations can be canonically understood as dual to orientations of biased graphs if and only if the underlying graph is planar.",

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KW - Cobiased graph

KW - single-element extension

KW - Orientation

KW - Duality

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EP - 213

JO - Journal of Combinatorial Mathematics and Combinatorial Computing

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