Recognizing even-cycle and even-cut matroids

Even-cycle matroids are elementary lifts of graphic matroids. Even-cut matroids are elementary lifts of cographic matroids. We give a polynomial time algorithm to check if a binary matroid is an even-cycle matroid. We also give a polynomial time algorithm to check if a binary matroid is an even-cut matroid. These algorithms rely on structural properties of the class of pinch-graphic matroids.

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