Regular Matroids with Graphic Cocircuits
Konstantinos Papalamprou (London School of Economics), Leonidas, Pitsoulis (Aristotle University of Thessaloniki)
TL;DR
This paper introduces the concept of graphic cocircuits in regular matroids and provides an algorithm to identify when cographic matroids with these cocircuits are signed-graphic, expanding understanding of matroid classifications.
Contribution
It defines graphic cocircuits in regular matroids and offers an algorithm to classify cographic matroids with these cocircuits as signed-graphic.
Findings
Large class of regular matroids with graphic cocircuits are signed-graphic
Algorithm determines whether a cographic matroid with graphic cocircuits is signed-graphic
Enhanced classification of matroids based on cocircuit properties
Abstract
We introduce the notion of graphic cocircuits and show that a large class of regular matroids with graphic cocircuits belongs to the class of signed-graphic matroids. Moreover, we provide an algorithm which determines whether a cographic matroid with graphic cocircuits is signed-graphic or not.
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Taxonomy
TopicsAdvanced Graph Theory Research · Graph Labeling and Dimension Problems · Advanced Combinatorial Mathematics