Kernelization of Two Path Searching Problems on Split Graphs

  • Yongjie Yang
  • Yash Raj Shrestha
  • Wenjun Li
  • Jiong Guo
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9711)


In the k-Vertex-Disjoint Paths problem, we are given a graph G and k terminal pairs of vertices, and are asked whether there is a set of k vertex-disjoint paths linking these terminal pairs, respectively. In the k-Path problem, we are given a graph and are asked whether there is a path of length k. It is known that both problems are NP-hard even in split graphs, which are the graphs whose vertices can be partitioned into a clique and an independent set. We study kernelization for the two problems in split graphs. In particular, we derive a 4k vertex-kernel for the k-Vertex-Disjoint Paths problem and a \(\frac{3}{2}k^2+\frac{1}{2}k\) vertex-kernel for the k-Path problem.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Yongjie Yang
    • 1
  • Yash Raj Shrestha
    • 2
  • Wenjun Li
    • 3
  • Jiong Guo
    • 4
  1. 1.Universität des SaarlandesSaarbrückenGermany
  2. 2.Department of Management, Technology and EconomicsETH ZürichZürichSwitzerland
  3. 3.Hunan Provincial Key Laboratory of Intelligent Processing of Big Data on Transportation, School of Computer and Communication EngineeringChangsha University of Science and TechnologyChangshaChina
  4. 4.School of Computer Science and TechnologyShandong UniversityShandongChina

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