Recognizing even-cycle and even-cut matroids

Even-cycle matroids are elementary lifts of graphic matroids and even-cut matroids are elementary lifts of cographic matroids. We present a polynomial algorithm to check if a binary matroid is an even-cycle matroid and we present a polynomial algorithm to check if a binary matroid is an even-cut matroid. These two algorithms rely on a polynomial algorithm (to be described in a pair of follow-up papers) to check if a binary matroid is pinch-graphic.