2013/12/19 by Carolyn Chun, Deborah Chun, Chun, Carolyn +5
Computer Science · #05B35 #Advanced Algebra and Logic #Advanced Graph Theory Research #Combinatorics (math.CO) #Constraint Satisfaction and Optimization #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1312.5401
openalex publication_date 2013/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
If S is a set of matroids, then the matroid M is S-fragile if, for every element e in E(M), either M\e or M/e has no minor isomorphic to a member of S. Excluded-minor characterizations often depend, implicitly or explicitly, on understanding classes of fragile matroids. In certain cases, when F is a minor-closed class of S-fragile matroids, and N is in F, the only members of F that contain N as a minor are obtained from N by increasing the length of fans. We prove that if this is the case, then we can certify it with a finite case-analysis. The analysis involves examining matroids that are at most two elements larger than N.