A method of graph reduction and its applications
-
Dmitrii V. Sirotkin
and
Dmitriy S. Malyshev
Abstract
The independent set problem for a given simple graph is to determine the size of a maximal set of its pairwise non-adjacent vertices. We propose a new way of graph reduction leading to a new proof of the NP-completeness of the independent set problem in the class of planar graphs and to the proof of NP-completeness of this problem in the class of planar graphs having only triangular internal facets of maximal vertex degree 18.
Originally published in Diskretnaya Matematika (2016) 28, №4, 114–125 (in Russian).
Acknowledgement
This work is supported by the Russian Science Foundation under grant 17-11-01336.
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Articles in the same Issue
- Frontmatter
- On the average-case complexity of underdetermined functions
- Combinatorial representations for the scheme of allocations of distinguishable particles into indistinguishable cells
- On groups containing the additive group of the residue ring or the vector space
- A method of graph reduction and its applications
- On the structure of digraphs of polynomial transformations over finite commutative rings with unity
Articles in the same Issue
- Frontmatter
- On the average-case complexity of underdetermined functions
- Combinatorial representations for the scheme of allocations of distinguishable particles into indistinguishable cells
- On groups containing the additive group of the residue ring or the vector space
- A method of graph reduction and its applications
- On the structure of digraphs of polynomial transformations over finite commutative rings with unity
