Above guarantee parameterization for vertex cover on graphs with maximum degree 4

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Abstract

In the vertex cover problem the input is a graph G and an integer k, and the goal is to decide whether there is a set of vertices S of size at most k such that every edge of G is incident on at least one vertex in S. We study the vertex cover problem on graphs with maximum degree 4 and minimum degree at least 2, parameterized by r= k- n/ 3. We give an algorithm for this problem whose running time is O(1. 6253 r). As a corollary, we obtain an O(1. 2403 k) -time algorithm for vertex cover on graphs with maximum degree 4.

Original languageEnglish
Article number34
JournalJournal of Combinatorial Optimization
Volume45
Issue number1
DOIs
StatePublished - 1 Jan 2023

Keywords

  • Graph algorithms
  • Parameterized complexity
  • Vertex cover

ASJC Scopus subject areas

  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Theory and Mathematics
  • Applied Mathematics

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