In unpublished work, Geelen proved that a matroid is near-regular if and only if it has no minor isomorphic to: U2,5; U3,5; the Fano plane and its dual; the non-Fano and its dual; the single-element deletion of AG(2,3), its dual, and the matroid obtained from it with a Delta-Y operation; and P8. We provide a proof of this characterization.
Additional Metadata
Keywords Matroids, Polynomials and Enumeration
THEME Logistics (theme 3)
Publisher Academic Press
Persistent URL dx.doi.org/10.1016/j.ejc.2011.01.013
Journal European Journal of Combinatorics
Project Matroid Structure for Efficiency
Citation
Hall, R, Mayhew, D, & van Zwam, S.H.M. (2011). The excluded minors for near-regular matroids. European Journal of Combinatorics, 32(6), 802–830. doi:10.1016/j.ejc.2011.01.013