M是连通拟阵与G（D#）是连通图的关系

The Relationship of Connected Matroid M and Connected Graph G（D#）

研究M是连通拟阵与G(D#)是连通图的关系。证明了M中有一个基B,使得C1,C2,…,Cn-r是M中全体对应于基B的基本极小圈,等价于对任意j∈1,2,…,n-r,Cj∪i≠jCi。由此证明了(Cunningham 1973,Krogdahl 1977)M是连通拟阵等价于B∪e∈E(M)-BCM(e,B),并且对任意X∩Y=φ,X∪Y=E(M)-B都有∪e∈XCMe,B∩∪e∈YCM(e,B)≠φ。得到结果为M是连通拟阵等价于G(D#)是连通图。

The relationship of connected matroid M and connected graph G（D#） is studied. First the propositio is n is proved that there is a base B in M, making C1, C2,..., Cn-r the fundamental circuit of M with respect to B, equivalent to the proposition that for any j∈{1,2,…,n-r},Cj￠∪i≠jCi. And then that （Cunningham 1973, Krogdahl 1977） M is a connected matroid is equivalent to Be∈E∪（M）-BCm（e,B）, and for any X∩Y=φ,X∪Y=E（M）-B,（e∈X∪Cm（e,B））∩（e∈Y∪Cm（e,B））≠φ . The main results of the paper is the equivalence of connected matroid M and connected graph G（D#）.