Dekel Tsur

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.