论文标题
排除的未成年人几乎是脆弱的II：基本要素
Excluded minors are almost fragile II: essential elements
论文作者
论文摘要
令$ m $作为$ \ mathbb {p} $的类别排除在某些部分字段$ \ mathbb {p} $中的代表矩阵，让$ n $是$ 3 $ 3 $连接的$ \ mathbb {p mathbb {p} $ - $ m $ m $ $ m $ $ m $ $ m \ backslash a，b $是$ 3 $与$ n $ -minor连接的。还假设$ | e（m）| \ geq | e（n）|+11 $和$ m \ backslash a，b $不是$ n $ fragile。在本文的前传中，我们证明了$ m \ backslash a，b $最多距离$ n $ fragile Minor的五个要素。如果$ m'/e $ $ $ $ $ $ $ n $ n $ n $ n $ n nes元素$ e $是$ n $ $ n $ n $ n $ n $ n $ n $ n $ n $'\ backslash e $ $ n $ n $ -minor。在本文中，我们证明，在温和的假设下，$ m \ backslash a，b $与至少$ r（m）-2 $元素（$ n $ exential-Essential-Extient）的未成年人距离是一个要素。
Let $M$ be an excluded minor for the class of $\mathbb{P}$-representable matroids for some partial field $\mathbb{P}$, let $N$ be a $3$-connected strong $\mathbb{P}$-stabilizer that is non-binary, and suppose $M$ has a pair of elements $\{a,b\}$ such that $M\backslash a,b$ is $3$-connected with an $N$-minor. Suppose also that $|E(M)| \geq |E(N)|+11$ and $M \backslash a,b$ is not $N$-fragile. In the prequel to this paper, we proved that $M \backslash a,b$ is at most five elements away from an $N$-fragile minor. An element $e$ in a matroid $M'$ is $N$-essential if neither $M'/e$ nor $M' \backslash e$ has an $N$-minor. In this paper, we prove that, under mild assumptions, $M \backslash a,b$ is one element away from a minor having at least $r(M)-2$ elements that are $N$-essential.
