Polynomial kernel for 2-Club Cluster Edge Deletion on general graphs

Establish whether 2-Club Cluster Edge Deletion on general graphs admits a polynomial-size kernel parameterized by the edge-deletion budget k.

Background

2-Club Cluster Edge Deletion asks whether at most k edges can be deleted so that every remaining connected component has diameter at most two. The paper notes that the problem is fixed-parameter tractable in general graphs, with a known algorithm running in O*(2.692^k) time, but that the existence of a polynomial kernel remains unresolved.

The paper studies restricted graph classes, obtaining polynomial kernels on interval graphs and split graphs. These results provide partial progress toward understanding whether comparable preprocessing is possible without structural restrictions on the input graph.