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arXiv · 1708.04536

Polynomial-time algorithms for the Longest Induced Path and Induced Disjoint Paths problems on graphs of bounded mim-width

Lars Jaffke·O-joung Kwon·Jan Arne Telle
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Abstract

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 $k$.

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Lars Jaffke, O-joung Kwon, Jan Arne Telle. 2017-08-15. Polynomial-time algorithms for the Longest Induced Path and Induced Disjoint Paths problems on graphs of bounded mim-width. https://arxiv.org/abs/1708.04536

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