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Circuits and cuts in binary matroids

Our paper titled Rainbow and monochromatic circuits and cuts in binary matroids has been accepted for publication in Discrete Mathematics! We show that if a binary matroid of rank r is colored with exactly r colors, then M either contains a rainbow colored circuit or a monochromatic cut. As the class of binary matroids is closed under taking duals, this immediately implies that if M is colored with exactly nr colors, then M either contains a rainbow colored cut or a monochromatic circuit. As a byproduct, one gets a characterization of binary matroids in terms of reductions to partition matroids.