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.
|Branch-width, Matroids, Graph minors, Grids|
|Matroids, geometric lattices (msc 05B35)|
|Journal of Combinatorial Theory - Series B|
|Organisation||Probability, Networks and Algorithms|
Geelen, J, Gerards, A.M.H, & Whittle, G. (2007). Excluding a planar graph from GF(q)-representable matroids. Journal of Combinatorial Theory - Series B, 97, 971–998.