Tuza's conjecture for binary geometries

Tuza (A conjecture, in Proceedings of the Colloquia Mathematica Societatis Janos Bolyai, 1981) conjectured that $τ(G) \le 2ν(G)$ for all graphs $G$, where $τ(G)$ is the minimum size of an edge set whose removal makes $G$ triangle-free, and $ν(G)$ is the maximum size of a collection of pairwise edge-disjoint triangles. Here, we generalise Tuza's conjecture to simple binary matroids that do not contain the Fano plane as a restriction. We prove that the geometric version of the conjecture holds for cographic matroids.

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