Matroids with a modular 4-point line

Abstract

A result of Seymour implies that any 3-connected matroid with a modular 3-point line is binary. We prove a similar characterization for 3-connected matroids with modular 4-point lines. We show that such a matroid is either representable over GF(3) or GF(4) or has an $F_7$-minor and either an $(F_7^{-})$- or $(F_7^{-}{)}^{\ast }$-minor.

arXiv comment26 pages

References in corpus (1)

• Representation of matroids with a modular plane