有界最小宽度图上最长诱导路和诱导不相交路问题的多项式时间算法
Polynomial-time algorithms for the Longest Induced Path and Induced Disjoint Paths problems on graphs of bounded mim-width
摘要：
我们给出了第一个多项式时间算法的图有界最大诱导匹配宽度（最小宽度）的问题，是不是局部检查。特别是，我们给$n^{\mathcal{O}(w)}$ -时间算法的最小宽度至多$w$，当给定的分解，为以下问题：最长诱导路径，诱导不相交的路径和$H$ -诱导拓扑子固定$H$。我们的结果意味着以下图类具有多项式时间算法这三个问题：区间和双区间图，圆弧，置换和循环置换图，凸图，$k$ -梯形，圆形$k$-梯形，$k$ -多边形，Dilworth- $k$和Co- $k$ -退化图固定$k$。
英文摘要：
We give the first polynomial-time algorithms on graphs of bounded maximum induced matching width (mim-width) for problems that are not locally checkable. In particular, we give $n^{\mathcal{O}(w)}$-time algorithms on graphs of mim-width at most $w$, when given a decomposition, for the following problems: Longest Induced Path, Induced Disjoint Paths and $H$-Induced Topological Minor for fixed $H$. Our results imply that the following graph classes have polynomial-time algorithms for these three problems: Interval and Bi-Interval graphs, Circular Arc, Permutation and Circular Permutation graphs, Convex graphs, $k$-Trapezoid, Circular $k$-Trapezoid, $k$-Polygon, Dilworth-$k$ and Co-$k$-Degenerate graphs for fixed $k$.
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。
