Classes of binary matroids with small lists of excluded induced minors
James Dylan Douthitt, James Oxley

TL;DR
This paper extends previous work by characterizing classes of binary matroids that exclude certain small minors as induced minors, providing a comprehensive understanding of their structural properties.
Contribution
It determines classes of matroids avoiding pairs of specific minors and advances the structural characterization of matroids excluding a particular minor.
Findings
Classified matroids avoiding pairs of minors such as M(C4) and M(K4)
Established structural lemmas for matroids excluding M(K4) as an induced minor
Extended the framework for understanding excluded induced minors in binary matroids
Abstract
In earlier work, we characterized the class of matroids with no as an induced minor and the class of matroids with no member of as an induced minor. In this paper, for every two matroids in , we determine the class of matroids that have neither of the chosen pair as an induced minor. Additionally, we prove structural lemmas toward characterizing the class of matroids that do not contain as an induced minor.
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Taxonomy
TopicsAdvanced Graph Theory Research · Advanced Algebra and Logic · Graph Labeling and Dimension Problems
