Kernelization algorithms for a generalization of the component order connectivity problem

In the component order connectivity problem, we are given a finite undirected graph G = (V,E) and non-negative integers k, ℓ. The goal of this problem is to determine whether there exists a subset S ⊆ V such that |S| ≤ k and the size of every connected component of the subgraph of G induced by V \ S is at most ℓ. In this paper, we consider the generalization of the component order connectivity problem where the condition on the sizes of connected components is generalized by non-decreasing subadditive functions defined on the subsets of V. We prove that the kernelization techniques for the component order connectivity problem proposed by Xiao can be generalized to our setting.