Journal of Combinatorial Theory Series B ( IF 1.2 ) Pub Date : 2021-04-23 , DOI: 10.1016/j.jctb.2021.04.002 Peter Nelson , Kazuhiro Nomoto
A simple binary matroid is called claw-free if none of its rank-3 flats are independent sets. These objects can be equivalently defined as the sets E of points in for which is not a basis of P for any plane P, or as the subsets X of containing no linearly independent triple for which .
We prove a decomposition theorem that exactly determines the structure of all claw-free matroids. The theorem states that claw-free matroids either belong to one of three particular basic classes of claw-free matroids, or can be constructed from these basic classes using a certain ‘join’ operation.
中文翻译:
无爪二元拟阵的结构
如果简单的二进制拟阵面中的第3级单位都不是独立的集合,则称为无爪类。这些对象可以被等效地定义为集合È在点 为此 不是的基P为任何平面P,或作为子集X的 不含线性独立的三元组 为此 。
我们证明了一个分解定理,该分解定理精确地确定了所有无爪类拟阵的结构。定理指出,无爪拟阵要么属于三种特定的无爪拟阵基本类之一,要么可以通过使用“联接”操作从这些基本类中构造出来。