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

Dekel Tsur ()
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Dekel Tsur: Ben-Gurion University of the Negev

Journal of Combinatorial Optimization, 2023, vol. 45, issue 1, No 39, 15 pages

Abstract: 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 $$r = k-n/3$$ r = k - n / 3 . We give an algorithm for this problem whose running time is $$O^*(1.6253^r)$$ O ∗ ( 1 . 6253 r ) . As a corollary, we obtain an $$O^*(1.2403^k)$$ O ∗ ( 1 . 2403 k ) -time algorithm for vertex cover on graphs with maximum degree 4.

Keywords: Vertex cover; Graph algorithms; Parameterized complexity (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10878-022-00966-8

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