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Kernelization of Two Path Searching Problems on Split Graphs

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Frontiers in Algorithmics (FAW 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9711))

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Abstract

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.

This work is supported by the National Natural Science Foundation of China under Grants (61502054).

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Authors and Affiliations

  1. Universität des Saarlandes, Saarbrücken, Germany

    Yongjie Yang

  2. Department of Management, Technology and Economics, ETH Zürich, Zürich, Switzerland

    Yash Raj Shrestha

  3. Hunan Provincial Key Laboratory of Intelligent Processing of Big Data on Transportation, School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha, China

    Wenjun Li

  4. School of Computer Science and Technology, Shandong University, Shandong, China

    Jiong Guo

Authors
  1. Yongjie Yang
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  2. Yash Raj Shrestha
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  3. Wenjun Li
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  4. Jiong Guo
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Corresponding author

Correspondence to Jiong Guo .

Editor information

Editors and Affiliations

  1. Shandong University, Jinan, China

    Daming Zhu

  2. MS EC-31, University of Texas at Dallas, Richardson, Texas, USA

    Sergey Bereg

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Yang, Y., Shrestha, Y.R., Li, W., Guo, J. (2016). Kernelization of Two Path Searching Problems on Split Graphs. In: Zhu, D., Bereg, S. (eds) Frontiers in Algorithmics. FAW 2016. Lecture Notes in Computer Science(), vol 9711. Springer, Cham. https://doi.org/10.1007/978-3-319-39817-4_23

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  • DOI: https://doi.org/10.1007/978-3-319-39817-4_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-39816-7

  • Online ISBN: 978-3-319-39817-4

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