A Polynomial Kernel for Trivially Perfect Editing

  • Pål Grønås Drange
  • Michał Pilipczuk
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9294)


We give a kernel with O(k7) vertices for Trivially Perfect Editing, the problem of adding or removing at most k edges in order to make a given graph trivially perfect. This answers in affirmative an open question posed by Nastos and Gao (Social Networks, 35(3):439–450, 2013) and by Liu, Wang, and Guo (Tsinghua Science and Technology, 19(4):346–357, 2014). Using our technique one can also obtain kernels of the same size for the related problems, Trivially Perfect Completion and Trivially Perfect Deletion.

We complement our study of Trivially Perfect Editing by proving that, contrary to Trivially Perfect Completion, it cannot be solved in time 2o(k)·nO(1) unless the Exponential Time Hypothesis fails. In this manner we complete the picture of the parameterized and kernelization complexity of the classic edge modification problems for the class of trivially perfect graphs.


Polynomial Kernel Reduction Rule Perfect Graph Edge Deletion Induce Subgraph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Dept. InformaticsUniv. BergenBergenNorway
  2. 2.Inst. InformaticsUniv. WarsawWarsawPoland

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