AN OBSTACLE TO A DECOMPOSITION THEOREM FOR NEAR-REGULAR MATROIDS

作者：Mayhew Dillon^*; Whittle Geoff; van Zwam Stefan H M

来源：SIAM Journal on Discrete Mathematics, 2011, 25(1): 271-279.

DOI：10.1137/090759616

• matroids
• decomposition
• partial fields

Seymour's decomposition theorem [J. Combin. Theory Ser. B, 28 (1980), pp. 305-359] for regular matroids states that any matroid representable over both GF(2) and 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 for other classes of matroids, notably for the class of near-regular matroids. Suppose that all near-regular matroids can be obtained from matroids that belong to a few basic classes through k-sums. Also suppose that these basic classes are such that, whenever a class contains all graphic matroids, it does not contain all cographic matroids. We show that, in that case, 3-sums will not suffice.

• 出版日期2011