Excluding a planar graph from GF(q)-representable matroids

Abstract. We prove that a binary matroid with huge branchwidth contains the cycle matroid of a large grid as a minor. This implies that an infinite antichain of binary matroids cannot contain the cycle matroid of a planar graph. The result also holds for any other finite field.

• Type: Journal
• Year: 2007
• Where: JCT
• Authors: Jim Geelen, Bert Gerards, Geoff Whittle
• Keywords: Huge Branchwidth, JCT 2007, Large Grid, Matroid