Let M and N be 3-connected matroids; we say that M is N-critical if M has an N-minor, but for each \(x\in E(M)\), \(M\backslash x\) is not 3-connected or \(M\backslash x\) has no N-minor. We establish that if M is an N-critical matroid with \(r^*(M)>\max \{3,r^*(N)\}\), then M has an element x such that either \(\mathrm{co}(M\backslash x)\) is N-critical or M has a coline \(L^*\) with \(|L^*|\ge 3\) such that \(M\backslash L^*\) is N-critical. As a corollary we get a chain theorem for the class of minimally 3-connected matroids. This chain theorem generalizes a previous one of Anderson and Wu for binary matroids.

令M和N为3个连接的拟阵；我们说如果M有N个小数，则M是N临界的，但是对于每个\ [x \ in E（M）\），\（M \反斜杠x \）没有3连接或\（M \反斜杠x \）没有N -minor。我们确定如果M是具有\（r ^ *（M）> \ max \ {3，r ^ *（N）\} \）的N临界拟阵，则M具有元素x使得\（\ mathrm {co}（M \反斜杠x）\）为N-临界值或M具有一条换行符\（L ^ * \）与\（| L ^ * | \ ge 3 \）使得\（M \反斜杠L ^ * \）为N-临界。作为推论，我们得到了极简三联类拟阵的一类链定理。这个链定理推广了Anderson和Wu的前一个关于二元拟阵。