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On the parameterized complexity of minimum/maximum degree vertex deletion on several special graphs

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Abstract

In the minimum degree vertex deletion problem, we are given a graph, a distinguished vertex in the graph, and an integer κ, and the question is whether we can delete at most κ vertices from the graph so that the distinguished vertex has the unique minimum degree. The maximum degree vertex deletion problem is defined analogously but here we want the distinguished vertex to have the unique maximum degree. It is known that both problems are NP-hard and fixed-parameter intractable with respect to some natural parameters. In this paper, we study the (parameterized) complexity of these two problems restricted to split graphs, p-degenerate graphs, and planar graphs. Our study provides a comprehensive complexity landscape of the two problems restricted to these special graphs.

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Acknowledgements

This work was supported by the Science and Education Joint Project of Hunan Natural Science Foundation (2021JJ60032), Research Foundation of Education Bureau of Hunan Province (21B0305), and Natural Science Foundation of Hunan Province of China (2022JJ30620).

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Authors and Affiliations

  1. School of Information Engineering, Hunan Industry Polytechnic, Changsha, 410036, China

    Jia Li

  2. 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, 410015, China

    Wenjun Li & Xueying Yang

  3. Chair of Economic Theory, Saarland University, Saarbrücken, 66123, Germany

    Yongjie Yang

Authors
  1. Jia Li
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  2. Wenjun Li
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  3. Yongjie Yang
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  4. Xueying Yang
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Corresponding author

Correspondence to Xueying Yang.

Additional information

Jia Li received a Master’s degree in computer technology from Hunan University, China in 2011. Now, she works in the School of Information Engineering, Hunan Industry Polytechnic, China. Her research interests include algorithms optimization and artificial intelligence.

Wenjun Li received the MSc and PhD degrees in computer science from Central South University, China in 2010 and 2014, respectively. He was a Visiting Scholar with the Department of Computing, Texas A&M University, USA from October 2011 to October 2012. He is currently an Associate Professor with the School of Computer and Communication Engineering, Changsha University of Science and Technology, China. His current research interests include algorithms optimization and artificial intelligence.

Yongjie Yang received the MSc degree in computer science from Central South University, China in 2011, and the PhD degree in computer science from Saarland University, Germany in 2015. He is currently a Postdoctoral Fellow with the Chair of Economic Theory, Saarland University, Germany. His current research interests include complexity analysis, algorithmic graph theory, game theory, and artificial intelligence.

Xueying Yang, Master of Computer Science. She received a bachelor’s degree in computer science in 2021 and is currently studying for a master’s degree in the School of Computer and Communication Engineering, Changsha University of Science and Technology, China. Her research interests include algorithms optimization and artificial intelligence.

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Li, J., Li, W., Yang, Y. et al. On the parameterized complexity of minimum/maximum degree vertex deletion on several special graphs. Front. Comput. Sci. 17, 174405 (2023). https://doi.org/10.1007/s11704-022-2200-8

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  • DOI: https://doi.org/10.1007/s11704-022-2200-8

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