2026-07-22T11:54:13Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:18158 2024-03-06T11:01:10Z ddc:004 open_access

Tight Bounds for Chordal/Interval Vertex Deletion Parameterized by Treewidth Włodarczyk, Michał fixed-parameter tractability treewidth chordal graphs interval graphs matroids representative families 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)⋅|V(G)|, improving upon the running time 2^𝒪(tw²)⋅|V(G)|^𝒪(1) by Jansen, de Kroon, and Włodarczyk (STOC'21). When a tree decomposition of width tw is given, then the base of the exponent equals 2^{ω-1}⋅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)⋅|V(G)|-time algorithm for Interval Vertex Deletion cannot be improved assuming Exponential Time Hypothesis. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Michał Włodarczyk 2023 Is Part Of LIPIcs, Volume 261, 50th International Colloquium on Automata, Languages, and Programming (ICALP 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ICALP.2023.106 urn:nbn:de:0030-drops-181585 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2023.106 eng https://creativecommons.org/licenses/by/4.0/legalcode