The highly connected even-cycle and even-cut matroids

TL;DR

This paper demonstrates that focusing on highly connected, sufficiently large matroids significantly reduces the number of excluded minors in classes like even-cycle and even-cut matroids, simplifying their structural analysis.

Contribution

It introduces a reduction in the complexity of classifying these matroids by considering only highly connected instances of sufficient size.

Findings

Number of excluded minors decreases when considering highly connected matroids.

Focus on connectivity simplifies the classification of even-cycle and even-cut matroids.

Results aid in understanding the structure of these matroid classes.

Abstract

The classes of even-cycle matroids, even-cycle matroids with a blocking pair, and even-cut matroids each have hundreds of excluded minors. We show that the number of excluded minors for these classes can be drastically reduced if we consider in each class only the highly connected matroids of sufficient size.