Problem Kernels for NP-Complete Edge Deletion Problems: Split and Related Graphs

In an edge deletion problem one is asked to delete at most k edges from a given graph such that the resulting graph satisfies a certain property. In this work, we study four NP-complete edge deletion problems where the goal graph has to be a chain, a split, a threshold, or a co-trivially perfect graph, respectively. All these four graph classes are characterized by a common forbidden induced subgraph 2K2, that is, an independent pair of edges. We present the seemingly first non-trivial algorithmic results for these four problems, namely, four polynomial-time data reduction algorithms that achieve problem kernels containing O(k), O(k), O(k), and O(k) vertices, respectively.