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

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  • Dekel Tsur

    (Ben-Gurion University of the Negev)

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.

Suggested Citation

  • Dekel Tsur, 2023. "Above guarantee parameterization for vertex cover on graphs with maximum degree 4," Journal of Combinatorial Optimization, Springer, vol. 45(1), pages 1-15, January.
    • Handle: RePEc:spr:jcomop:v:45:y:2023:i:1:d:10.1007_s10878-022-00966-8
    DOI: 10.1007/s10878-022-00966-8
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    References listed on IDEAS

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    1. Mingyu Xiao & Hiorshi Nagamochi, 2017. "A refined algorithm for maximum independent set in degree-4 graphs," Journal of Combinatorial Optimization, Springer, vol. 34(3), pages 830-873, October.
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