Geodesic
A method of graph reduction and its applications
Diskretnaya Matematika, Tome 29 (2017) no. 3, pp. 114-125.

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The independent set problem for a given simple graph is to determine the size of a maximum 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.
Keywords: independent sets, planar graph, planar triangulation, computational complexity. 
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D. V. sirotkin; D. S. Malyshev. A method of graph reduction and its applications. Diskretnaya Matematika, Tome 29 (2017) no. 3, pp. 114-125. http://geodesic.mathdoc.fr/item/DM_2017_29_3_a7/

[1] Alekseev V.E., “O szhimaemykh grafakh”, Problemy kibernetiki, 36 (1979), 23–31, Iz-vo «Nauka», Moskva

[2] Alekseev V.E., “O vliyanii lokalnykh ogranichenii na slozhnost opredeleniya chisla nezavisimosti grafa”, Kombinatorno-algebraicheskie metody v prikladnoi matematike, 1983, 3–13, Iz-vo Gorkovskogo gos. universiteta, Gorkii

[3] Alekseev V.E., Lozin V.V., “O lokalnykh preobrazovaniyakh grafov, sokhranyayuschikh chislo nezavisimosti”, Diskretnyi analiz i issledovanie operatsii, 5:1 (1998), 3–19 | MR | Zbl

[4] Kobylkin K.S., “Vychislitelnaya slozhnost zadachi vershinnogo pokrytiya v klasse planarnykh triangulyatsii”, Trudy in-ta matem. i mekh. UrO RAN, 22:3 (2016), 153–159 | MR

[5] Alekseev V.E., Malyshev D.S., “Planar graph classes with the independent set problem solvable in polynomial time”, J. Appl. Industr. Math., 3:1 (2008), 1–5 | DOI | MR

[6] Garey M.R., Johnson D.S., Stockmeyer L., “Some simplified NP-complete graph problems”, Theor. Comput. Sci., 1:3 (1976), 237–267 | DOI | MR | Zbl

[7] Hopcroft J., Tarjan R.E., “Efficient planarity testing”, ACM, 21:4 (1974), 549–568 | MR | Zbl

[8] Lozin V.V., Milanic M., “On the maximum independent set problem in subclasses of planar graphs”, J. Graph Algor. Appl., 14:2 (2010), 269–286 | DOI | MR | Zbl

[9] Lozin V.V., Monnot J., Ries B., “On the maximum independent set problem in subclasses of subcubic graphs”, J. Discr. Algor., 31 (2015), 104–112 | DOI | MR | Zbl

[10] Malyshev D.S., “Classes of subcubic planar graphs for which the independent set problem is polynomially solvable”, J. Appl. Industr. Math., 7:4 (2013), 537–548 | DOI | Zbl