Given a rank-$r$ binary matroid we construct a system of $O(r^3)$ linear equations in $O(r^3)$ variables that has a solution over GF$(2)$ if and only if the matroid is graphic.
Additional Metadata
Keywords Matroids, Graphc Matroids, Planar Graphs
MSC Matroids, geometric lattices (msc 05B35)
THEME Other (theme 6)
Publisher Academic Press
Persistent URL dx.doi.org/10.1016/j.jctb.2013.07.00
Journal Journal of Combinatorial Theory - Series B
Citation
Geelen, J, & Gerards, A.M.H. (2013). Characterizing graphic matroids by a system of linear equations. Journal of Combinatorial Theory - Series B, 103(5), 642–646. doi:10.1016/j.jctb.2013.07.00