An Improved Fixed-Parameter Algorithm for 2-Club Cluster Edge Deletion

A 2-club is a graph of diameter at most two. In the decision version 2-Club Cluster Edge Deletion problem, an undirected G given along with integer k≥0 as parameter, and question whether can be transformed into disjoint union 2-clubs by deleting k edges. simple fixed-parameter algorithm solves problem in O⁎(3k), decade-old improved this running to O⁎(2.74k) time via more sophisticated case analysis. Unfortunately, latter shown have flawed branching scenario. that breaks 3k barrier presented paper, O⁎(2.692k). This also improves previously claimed time.