Improved kernel and algorithm for claw and diamond free edge deletion based on refined observations

Abstract

In the ▪-Free Edge Deletion problem (CDFED), we are given a graph G and an integer k>0, and the question is whether there are at most k edges whose deletion results in a graph without claws and diamonds as induced subgraphs. Based on some refined observations, we propose a kernel of O(k3) vertices and O(k4) edges, significantly improving the previous kernel of O(k12) vertices and O(k24) edges. In addition, we derive an O⁎(3.792k)-time algorithm for CDFED.