标题： 圆图作为顶点minor的Erdős-Pósa性质 显示英文标题

标题： The Erdős-Pósa property for circle graphs as vertex-minors

摘要： 我们证明了对于任意至少有一条边的圆图$H$和任意正整数$k$，存在一个整数$t=t(k,H)$，使得每个图$G$要么有一个与$k$个$H$的不相交并集同构的顶点minor，要么有一个与$t$-扰动相关的图且没有与$H$同构的顶点minor。 利用相同的技术，我们还证明了对于任意平面多重图 $H$，每个二元拟阵要么有一个与 $kH$的圈拟阵同构的子拟阵，要么是一个低秩扰动的二元拟阵，并且没有与 $H$的圈拟阵同构的子拟阵。 显示英文摘要

摘要： We prove that for any circle graph $H$ with at least one edge and for any positive integer $k$, there exists an integer $t=t(k,H)$ so that every graph $G$ either has a vertex-minor isomorphic to the disjoint union of $k$ copies of $H$, or has a $t$-perturbation with no vertex-minor isomorphic to $H$. Using the same techniques, we also prove that for any planar multigraph $H$, every binary matroid either has a minor isomorphic to the cycle matroid of $kH$, or is a low-rank perturbation of a binary matroid with no minor isomorphic to the cycle matroid of $H$.