Given a rank-r binary matroid we construct a system of $O(r^3)$ linear equations in $O(r^2)$ variables that has a solution over GF(2) if and only if the matroid is graphic.

Additional Metadata
Keywords matroids, graphic matroids, planar graphs
MSC Matroids, geometric lattices (msc 05B35)
THEME Logistics (theme 3)
Series preprint (not CWI, to be used with submitted papers)
Project Matroid Structure for Efficiency
Citation
Geelen, J, & Gerards, A.M.H. (2011). Characterizing graphic matroids by a system of linear equations. preprint (not CWI, to be used with submitted papers).