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Improved Kernels for Several Problems on Planar Graphs

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Book cover Frontiers in Algorithmics (FAW 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10823))

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Abstract

In this paper, we study the kernelization of the Induced Matching problem on planar graphs, the Parameterized Planar 4-Cycle Transversal problem and the Parameterized Planar Edge-Disjoint 4-Cycle Packing problem. For the Induced Matching problem on planar graphs, based on Gallai-Edmonds structure, a kernel of size 26k is presented, which improves the current best result 28k. For the Parameterized Planar 4-Cycle Transversal problem, by partitioning the vertices in given instance into four parts and analyzing the size of each part independently, a kernel with at most \(51k-22\) vertices is obtained, which improves the current best result 74k. Based on the kernelization process of the Parameterized Planar 4-Cycle Transversal problem, a kernel of size \(51k-22\) can also be obtained for the Parameterized Planar Edge-Disjoint 4-Cycle Packing problem, which improves the current best result 96k.

This work is supported by the National Natural Science Foundation of China under Grants (61420106009, 61232001, 61472449, 61672536).

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Authors and Affiliations

  1. School of Information Science and Engineering, Central South University, Changsha, 410083, People’s Republic of China

    Qilong Feng, Beilin Zhuo, Guanlan Tan, Neng Huang & Jianxin Wang

Authors
  1. Qilong Feng
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  2. Beilin Zhuo
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  3. Guanlan Tan
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  4. Neng Huang
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  5. Jianxin Wang
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Correspondence to Jianxin Wang .

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Editors and Affiliations

  1. Texas A&M University, College Station, Texas, USA

    Jianer Chen

  2. Shanghai University of Finance and Economics, Shanghai, China

    Pinyan Lu

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Feng, Q., Zhuo, B., Tan, G., Huang, N., Wang, J. (2018). Improved Kernels for Several Problems on Planar Graphs. In: Chen, J., Lu, P. (eds) Frontiers in Algorithmics. FAW 2018. Lecture Notes in Computer Science(), vol 10823. Springer, Cham. https://doi.org/10.1007/978-3-319-78455-7_13

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  • DOI: https://doi.org/10.1007/978-3-319-78455-7_13

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