论文标题
三类具有特殊类型的天然曲霉的两类2类玻璃体的未成年人
The excluded minors for three classes of 2-polymatroids having special types of natural matroids
论文作者
论文摘要
如果$ \ Mathcal {c} $是一类较小的曲霉类，则$ \ Mathcal {c} $ of Integer polymatroids的天然矩形在$ \ mathcal {c} $中也是较小的，也是较小的，也是较小的关闭$ \ MATHCAL {C}'$。 We find the excluded minors for $\mathcal{C}'_2$ when $\mathcal{C}$ is (i) the class of binary matroids, (ii) the class of matroids with no $M(K_4)$-minor, and, combining those, (iii) the class of matroids whose connected components are cycle matroids of series-parallel networks.在每种情况下，类$ \ MATHCAL {C} $有限地排除了许多未成年人，但是仅在（II）的情况下，$ \ Mathcal {C}'_ 2 $是正确的。我们还介绍了$ k $ - 自然的Matroid，这是$ k $ - 甲状腺素的天然基质体的一种变体，并用它来证明这些2-脊椎动物的类别在二维下关闭。
If $\mathcal{C}$ is a minor-closed class of matroids, the class $\mathcal{C}'$ of integer polymatroids whose natural matroids are in $\mathcal{C}$ is also minor closed, as is the class $\mathcal{C}'_k$ of $k$-polymatroids in $\mathcal{C}'$. We find the excluded minors for $\mathcal{C}'_2$ when $\mathcal{C}$ is (i) the class of binary matroids, (ii) the class of matroids with no $M(K_4)$-minor, and, combining those, (iii) the class of matroids whose connected components are cycle matroids of series-parallel networks. In each case the class $\mathcal{C}$ has finitely many excluded minors, but that is true of $\mathcal{C}'_2$ only in case (ii). We also introduce the $k$-natural matroid, a variant of the natural matroid for a $k$-polymatroid, and use it to prove that these classes of 2-polymatroids are closed under 2-duality.
