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Characterizing graphic matroids by a system of linear equations. (English) Zbl 1408.05029
Summary: 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.

MSC:
05B35 Combinatorial aspects of matroids and geometric lattices
52B40 Matroids in convex geometry (realizations in the context of convex polytopes, convexity in combinatorial structures, etc.)
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