Abstract
A biased graph Φ consists of a graph and a class of distinguished polygons such that no theta subgraph contains exactly two distinguished polygons. There are three matroids naturally associated with Φ: the bias matroid G( Φ), the lift matroid L( Φ), and the complete lift L 0( Φ). We characterize those Φ for which any of these matroids is binary.
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