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arXiv · 2305.03440

Tight Bounds for Chordal/Interval Vertex Deletion Parameterized by Treewidth

Michal Wlodarczyk
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Abstract

In Chordal/Interval Vertex Deletion we ask how many vertices one needs to remove from a graph to make it chordal (respectively: interval). We study these problems under the parameterization by treewidth $tw$ of the input graph $G$. On the one hand, we present an algorithm for Chordal Vertex Deletion with running time $2^{O(tw)} \cdot |V(G)|$, improving upon the running time $2^{O(tw^2)} \cdot |V(G)|^{O(1)}$ by Jansen, de Kroon, and Wlodarczyk (STOC'21). When a tree decomposition of width $tw$ is given, then the base of the exponent equals $2^{\omega-1}\cdot 3 + 1$. Our algorithm is based on a novel link between chordal graphs and graphic matroids, which allows us to employ the framework of representative families. On the other hand, we prove that the known $2^{O(tw \log tw)} \cdot |V(G)|$-time algorithm for Interval Vertex Deletion cannot be improved assuming Exponential Time Hypothesis.

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Michal Wlodarczyk. 2023-05-05. Tight Bounds for Chordal/Interval Vertex Deletion Parameterized by Treewidth. https://doi.org/10.1007/s00453-025-01293-0

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