Detecting minors in matroids through triangles
Boris Albar, Daniel Gon\c{c}alves, Jorge L. Ram\'irez Alfons\'in
TL;DR
This paper explores conditions involving triangles in matroids that guarantee the presence of specific minors such as U_{2,4}, F_7, or M(K_5), advancing understanding of matroid minor structures.
Contribution
It introduces new sufficient conditions based on triangles for detecting certain minors in matroids, contributing to matroid theory.
Findings
Identifies triangle-based conditions for minors U_{2,4}, F_7, M(K_5)
Provides theoretical criteria for matroid minor detection
Enhances structural understanding of matroids through triangles
Abstract
In this note we investigate some matroid minor structure results. In particular, we present sufficient conditions, in terms of {\em triangles}, for a matroid to have either or or as a minor.
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Taxonomy
TopicsAdvanced Graph Theory Research · Structural Analysis and Optimization · Computational Geometry and Mesh Generation