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.
|Issue number||1812.10808 [cs.DS]|
|State||Published - 2018|