- Title
- Small separations in pinch-graphic matroids
- KIAS Author
- Heo, Cheolwon
- Journal
- MATHEMATICAL PROGRAMMING, 2024
- Abstract
- Even-cycle matroids are elementary lifts of graphic matroids. Pinch-graphic matroids are even-cycle matroids that are also elementary projections of graphic matroids. In this paper we analyze the structure of 1-, 2-, and 3-separations in these matroids. As a corollary we obtain a polynomial-time algorithm that reduces the problem of recognizing pinch-graphic matroids to internally 4-connected matroids. Combining this with earlier results (Guenin and Heo in Recognizing even-cycle and even-cut matroids manuscript, 2020; Guenin and Heo in Recognizing pinch-graphic matroids manuscript, 2020) we obtain a polynomial-time algorithm for recognizing even-cycle matroids and we obtain a polynomial-time algorithm for recognizing even-cut matroids.