Whitney交换的核化
Kernelization of Whitney Switches
摘要：
Whitney在1933年的一个基本定理证明了2-连通图G和H是2-同构的，或者等价地说，它们的圈拟阵是同构的，当且仅当G可以通过一系列称为Whitney开关的运算转化为H。在本文中，我们考虑的定量问题所产生的惠特尼定理：给定两个2-同构图，我们可以转换成另一个应用最多k惠特尼开关？这个问题已经是NP-完全的周期，我们研究其参数化的复杂性。我们证明了这个问题允许一个大小为O（k）的核，因此，当用k参数化时，是固定参数易处理的。
英文摘要：
A fundamental theorem of Whitney from 1933 asserts that 2-connected graphs G and H are 2-isomorphic, or equivalently, their cycle matroids are isomorphic, if and only if G can be transformed into H by a series of operations called Whitney switches. In this paper we consider the quantitative question arising from Whitney's theorem: Given two 2-isomorphic graphs, can we transform one into another by applying at most k Whitney switches? This problem is already NP-complete for cycles, and we investigate its parameterized complexity. We show that the problem admits a kernel of size O(k), and thus, is fixed-parameter tractable when parameterized by k.
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。
