Polynomial-time solvability of the independent set problem in a certain class of subcubic planar graphs
The independent set problem for a given simple graph consists in computing the size of a largest subset of its pairwise nonadjacent vertices. In this article, we prove the polynomial solvability of the problem for the subcubic planar graphs with no induced tree obtained by identifying the ends of three paths of lengths 3, 3, and 2 respectively.
Keywordsindependent set problem graph reduction efficient algorithm
Unable to display preview. Download preview PDF.
- 1.V. E. Alekseev, “On Compressible Graphs,” in Problems of Cybernetics, Vol. 36 (Nauka, Moscow, 1979), pp. 23–31.Google Scholar
- 6.V. E. Alekseev, V. V. Lozin, D. S. Malyshev, and M. Milanič, “The Maximum Independent Set Problem in Planar Graphs,” in Mathematical Foundations of Computer Science 2008: Proceedings of 33rd International Symposium MFCS, Torun´, Poland, August 25–29, 2008 (Springer, Heidelberg, 2008), pp. 96–107.CrossRefGoogle Scholar
- 8.V. V. Lozin and M. Milanič, “Maximum Independent Sets in Graphs of Low Degree,” in Proceedings of 18th Annual ACM-SIAM Symposium on Discrete Algorithms, New Orleans, USA, January 7–9, 2007 (SIAM, Philadelphia, PA, 2007), pp. 874–880.Google Scholar