An Obstacle to a Decomposition Theorem for Near-Regular Matroids
An Obstacle to a Decomposition Theorem for Near-Regular Matroids
Seymour's decomposition theorem [J. Combin. Theory Ser. B, 28 (1980), pp. 305–359] for regular matroids states that any matroid representable over both $\mathrm{GF}(2)$ and $\mathrm{GF}(3)$ can be obtained from matroids that are graphic, cographic, or isomorphic to $R_{10}$ by 1-, 2-, and 3-sums. It is hoped that similar characterizations hold …