2015/11/09 by Ben Clark, Clark, Ben, Dillon Mayhew +5
Computer Science · #05B35 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Interconnection Networks and Systems
paper · pdf · doi:10.48550/arxiv.1511.02840
openalex publication_date 2015/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let N be a set of matroids. A matroid M is strictly N-fragile if M has a member of N as minor and, for all e ∈ E(M), at least one of M\backslash e and M/e has no minor in N. In this paper we give a structural description of the strictly \U2,5,U3,5\-fragile matroids that have six inequivalent representations over GF(5). Roughly speaking, these matroids fall into two classes. The matroids without an \X8, Y8, Y8*\-minor are constructed, up to duality, from one of two matroids by gluing wheels onto specified triangles. On the other hand, those matroids with an \X8, Y8, Y8*\-minor can be constructed from a matroid in \X8, Y8, Y8*\ by repeated application of elementary operations, and are shown to have path width 3. The characterization presented here will be crucial in finding the explicit list of excluded minors for two classes of matroids: the Hydra-5-representable matroids and the 2-regular matroids.