Computational complexity on interval graphs

Determine whether 2-Club Cluster Edge Deletion on interval graphs is solvable in polynomial time or is NP-complete on this graph class.

Background

The paper establishes a polynomial vertex kernel of size O(k^5) for 2-Club Cluster Edge Deletion on interval graphs, but kernelization does not resolve the problem’s classical computational complexity.

The authors explicitly identify the unresolved distinction between the existence of a polynomial-time algorithm and NP-completeness on interval graphs. This remains open despite the fact that the corresponding Cluster Edge Deletion problem, with diameter bound one, is polynomial-time solvable on interval graphs.