顶点子式与轴子式的交织连通性
Intertwining connectivities for vertex-minors and pivot-minors
AI总结：
本文证明了在足够大的图中，可通过顶点子式操作移除某顶点并保持两对顶点集间的交织连通性，该结果蕴含了二元拟阵上的类似定理。
摘要：
我们证明，对于图$G$的顶点不相交子集对$(Q,R)$和$(S,T)$，若$G$足够大，则存在顶点$v\in V(G)-(Q\cup R\cup S\cup T)$，使得能通过移除$v$的顶点子式操作以两种方式化简$G$，同时保持$Q$与$R$及$S$与$T$之间的连通性。我们的定理蕴含了Chen和Whittle（2014）关于拟阵限制在二元拟阵上的类似定理。
英文摘要：
We show that for pairs $(Q,R)$ and $(S,T)$ of disjoint subsets of vertices of a graph $G$, if $G$ is sufficiently large, then there exists a vertex $v$ in $V(G)-(Q\cup R\cup S\cup T)$ such that there are two ways to reduce $G$ by a vertex-minor operation that removes $v$ while preserving the connectivity between $Q$ and $R$ and the connectivity between $S$ and $T$. Our theorem implies an analogous theorem of Chen and Whittle (2014) for matroids restricted to binary matroids.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
