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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.

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Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

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  1. Department of computer science, Ben-Gurion University of the Negev, Beersheba, Israel

    Dekel Tsur

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  1. Dekel Tsur
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Correspondence to Dekel Tsur.

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Tsur, D. Above guarantee parameterization for vertex cover on graphs with maximum degree 4. J Comb Optim 45, 34 (2023). https://doi.org/10.1007/s10878-022-00966-8

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