Faster parameterized algorithms for two vertex deletion problems

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In the l-PATH VERTEX COVER problem (resp., the l-COMPONENT ORDER CONNECTIVITY problem) the input is an undirected graph G and an integer k. The goal is to decide whether there is a set of vertices of size at most k whose deletion from G results in a graph that does not contain a path with l vertices (resp., does not contain a connected component with at least l vertices). In this paper we give a parameterized algorithm for l-PATH VERTEX COVER when l=5,6,7, whose running times are O(3.945k), O(4.947k), and O(5.951k), respectively. We also give an algorithm for l-COMPONENT ORDER CONNECTIVITY whose running time is O((l−1−ϵl)k) for every l≥4, where ϵl>0 for every l.

Original languageEnglish
Pages (from-to)112-123
Number of pages12
JournalTheoretical Computer Science
StatePublished - 9 Jan 2023


  • Graph algorithms
  • Parameterized complexity

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science


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