A notion of minor-based matroid connectivity
A notion of minor-based matroid connectivity
复制标题
基于次要拟阵连接的概念
DOI：
10.1016/j.aam.2018.07.001
复制
发表时间：
2017
影响因子：
1.1
通讯作者：
James G. Oxley
中科院分区：
文献类型：
--
作者：
Zachary Gershkoff;James G. Oxley
对于拟阵N，如果M的每两个元素都在N-子阵中，则拟阵M是N-连通的。因此拟阵是连通的当且仅当它是U1，2-连通的。证明了U1，2是唯一连通的拟阵N，使得如果M与|E(M)|和|E(N)|N-连通，则M\e或M/e对所有元素e都是N-连通的.此外，我们还证明了U1，2和M(W2)是唯一的拟阵N使得，当一个拟阵有一个使用{e，f}的N-子阵和一个使用{f，g}的N-子阵时，它也有一个使用{e，g}的N-子阵.最后，我们证明了M是U0，1⊕U1，1-连通的当且仅当M的每个克隆类都是平凡的。
For a matroid N, a matroid M is N-connected if every two elements of M are in an N-minor together. Thus a matroid is connected if and only if it is U 1, 2-connected. This paper proves that U 1, 2 is the only connected matroid N such that if M is N-connected with| E (M)|>| E (N)|, then M\e or M/e is N-connected for all elements e. Moreover, we show that U 1, 2 and M (W 2) are the only matroids N such that, whenever a matroid has an N-minor using {e, f} and an N-minor using {f, g}, it also has an N-minor using {e, g}. Finally, we show that M is U 0, 1⊕ U 1, 1-connected if and only if every clonal class of M is trivial.