Excluding a planar graph from GF(q)-representable matroids
Journal of Combinatorial Theory - Series B , Volume 97 p. 971- 998
We prove that a binary matroid with huge branch-width 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.