On the Maximum Independent Set Problem in Graphs of Bounded Maximum Degree

Abstract

We consider the maximum independent set (MIS) problem, i.e., the problem asking for a vertex subset of maximum cardinality of a graph such that no two vertices in this set are adjacent. The problem is known to be NP-hard in general, even if restricted on graphs of maximum degree at most Δ for a given integer Δ ≥ 3, i.e., every vertex is of degree at most Δ. We try to figure out some bounded maximum degree graph classes, under which the problem can be solved in polynomial time.

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Acknowledgments

This research is supported by the National Foundation for Science and Technology Development (NAFOSTED) of Vietnam, project code: 101.99-2016.20. The manuscript has been finished in the time the first author was in Vietnam Institute for Advanced Studies in Mathematics, Year 2018 and has been revised in the time the first author was in Institute of Mathematics, Vietnam Academy of Science and Technology, Year 2019. The authors would like to thank to all received supports. We also want to express the appreciation to the anonymous referees and the editors for their very useful advices, comments, and corrections.

Funding

The first author receives funding from Vietnamese Institute for Advanced Studies in Mathematics, from 03-04/2018.

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Correspondence to Ngoc C. Lê.

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Dedicated to Professor Hoang Tuy

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Lê, N.C., Tran, T. On the Maximum Independent Set Problem in Graphs of Bounded Maximum Degree. Acta Math Vietnam 45, 463–475 (2020). https://doi.org/10.1007/s40306-020-00368-0

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Keywords

  • Maximum independent set
  • Stable set
  • Low degree graph

Mathematics Subject Classification (2010)

  • 05C85