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.
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
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