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

Dekel Tsur

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

Department of Computer Science

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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∗(1.6253r). As a corollary, we obtain an O∗(1.2403k)-time algorithm for vertex cover on graphs with maximum degree 4.

Original language	English
Journal	Arxiv preprint
Issue number	1812.10808 [cs.DS]
State	Published - 2018

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title = "Above guarantee parameterization for vertex cover on graphs with maximum degree 4.",

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∗(1.6253r). As a corollary, we obtain an O∗(1.2403k)-time algorithm for vertex cover on graphs with maximum degree 4. ",

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PY - 2018

Y1 - 2018

N2 - 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∗(1.6253r). As a corollary, we obtain an O∗(1.2403k)-time algorithm for vertex cover on graphs with maximum degree 4.

AB - 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∗(1.6253r). As a corollary, we obtain an O∗(1.2403k)-time algorithm for vertex cover on graphs with maximum degree 4.

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JO - arXiv preprint

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

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