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On the Maximum Independent Set Problem in Subclasses of Subcubic Graphs

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 8288)

Abstract

It is known that the maximum independent set problem is NP-complete for subcubic graphs, i.e. graphs of vertex degree at most 3. Moreover, the problem is NP-complete for H-free subcubic graphs whenever H contains a connected component which is not a tree with at most 3 leaves. We show that if every connected component of H is a tree with at most 3 leaves and at most 7 vertices, then the problem can be solved for H-free subcubic graphs in polynomial time.

Keywords

  • Independent set
  • Polynomial-time algorithm
  • Subcubic graph

The first author gratefully acknowledges support from DIMAP - the Center for Discrete Mathematics and its Applications at the University of Warwick, and from EPSRC, grant EP/I01795X/1.

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Lozin, V., Monnot, J., Ries, B. (2013). On the Maximum Independent Set Problem in Subclasses of Subcubic Graphs. In: Lecroq, T., Mouchard, L. (eds) Combinatorial Algorithms. IWOCA 2013. Lecture Notes in Computer Science, vol 8288. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-45278-9_27

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  • DOI: https://doi.org/10.1007/978-3-642-45278-9_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-45277-2

  • Online ISBN: 978-3-642-45278-9

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