Improved Kernels and Algorithms for Claw and Diamond Free Edge Deletion Based on Refined Observations

Abstract

In the {Claw, Diamond}-Free Edge Deletion problem, we are given a graph G and an integer k > 0, the question is whether there are at most k edges whose deletion results in a graph without claws and diamonds as induced graphs. Based on some refined observations, we propose a kernel of O(k 3 ) vertices and O(k 4 ) edges, significantly improving the previous kernel of O(k 12 ) vertices and O(k 24 ) edges. In addition, we derive an O * (3.792 k )-time algorithm for the {Claw, Diamond}-Free Edge Deletion problem.

An algorithm for destroying claws and diamonds

“…The problem has a simple O * (5 k )-time algorithm [1]. Li et al [4] gave an O(3.792 k )-time algorith. In this paper we give an algorithm for whose running time is O * (3.562 k ).…”