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

  • Jiong Guo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4835)


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 2K 2, 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 2), O(k 4), O(k 3), and O(k 3) vertices, respectively.


Bipartite Graph Graph Class Perfect Graph Split Graph Discrete Apply Mathematic 
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© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Jiong Guo
    • 1
  1. 1.Institut für Informatik, Friedrich-Schiller-Universität Jena, Ernst-Abbe-Platz 2, D-07743 JenaGermany

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