论文标题
三连接的曲霉中的弹性元素
Elastic elements in 3-connected matroids
论文作者
论文摘要
从比克斯比的引理出发，如果$ e $是$ 3 $连接的Matroid $ m $的元素，则是$ {\ rm co}（m \ delete e）$，$ m \ m \ delete e $的cosimplification of $ m \ delete e $，或$ {\ rm si}（m/e）（m/e）$，$ m/e $，是$ -M/e $，是$ -M/e $，IS $ 3 $ 3.3 $ 33 $ 3 $ 3.3 $ 3 $ 3.3 $ 3.3 $ 3.3 $ 3 $ 3.一个自然的问题是，$ m $是否具有元素$ e $，使得$ {\ rm co}（m \ delete e）$和$ {\ rm si}（m/e）$均为$ 3 $连接。称这种元素为“弹性”，在本文中，我们表明，如果$ | e（m）| \ ge 4 $，那么$ m $至少具有四个弹性元素，因为$ m $有$ 4 $ element的粉丝，而且，$ m $ no $ 3 $ 3 $ neparate的$ s $是$ 2 $ $ 2 $ $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2 $ 2是对某个成员的成员或单元素删除的同构。
It follows by Bixby's Lemma that if $e$ is an element of a $3$-connected matroid $M$, then either ${\rm co}(M\delete e)$, the cosimplification of $M\delete e$, or ${\rm si}(M/e)$, the simplification of $M/e$, is $3$-connected. A natural question to ask is whether $M$ has an element $e$ such that both ${\rm co}(M\delete e)$ and ${\rm si}(M/e)$ are $3$-connected. Calling such an element "elastic", in this paper we show that if $|E(M)|\ge 4$, then $M$ has at least four elastic elements provided $M$ has no $4$-element fans and, up to duality, $M$ has no $3$-separating set $S$ that is the disjoint union of a rank-$2$ subset and a corank-$2$ subset of $E(M)$ such that $M|S$ is isomorphic to a member or a single-element deletion of a member of a certain family of matroids.
