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 language | American English |
|---|---|
| Article number | 34 |
| Journal | Journal of Combinatorial Optimization |
| Volume | 45 |
| Issue number | 1 |
| DOIs | |
| State | Published - 1 Jan 2023 |
Keywords
- Graph algorithms
- Parameterized complexity
- Vertex cover
All Science Journal Classification (ASJC) codes
- Computer Science Applications
- Discrete Mathematics and Combinatorics
- Control and Optimization
- Computational Theory and Mathematics
- Applied Mathematics