The Maximum Independent Set Problem in Planar Graphs

Authors:
Vladimir E. Alekseev;Vadim Lozin;Dmitriy Malyshev;Martin Milanič
Affiliations:
Department of Computational Mathematics, Nizhny Novgorod University, Russia;DIMAP and Mathematics Institute, University of Warwick, Coventry, UK;Department of Computational Mathematics, Nizhny Novgorod University, Russia;AG Genominformatik, Faculty of Technology, Bielefeld University, Germany
Venue:
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Year:
2008

Citing 10
Cited 0

Graph minors. V. Excluding a planar graph

Journal of Combinatorial Theory Series B
Linear time algorithms for NP-hard problems restricted to partial k-trees

Discrete Applied Mathematics
Computing independent sets in graphs with large girth

Discrete Applied Mathematics
The four-colour theorem

Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday
A partial k-arboretum of graphs with bounded treewidth

Theoretical Computer Science
Polynomial algorithm for finding the largest independent sets in graphs without forks

Discrete Applied Mathematics
A polynomial algorithm to find an independent set of maximum weight in a fork-free graph

SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Maximum independent sets in graphs of low degree

SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Recent developments on graphs of bounded clique-width

Discrete Applied Mathematics
Independent sets in extensions of 2K2-free graphs

Discrete Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

We study the computational complexity of finding a maximum independent set of vertices in a planar graph. In general, this problem is known to be NP-hard. However, under certain restrictions it becomes polynomial-time solvable. We identify a graph parameter to which the complexity of the problem is sensible and produce a number of both negative (intractable) and positive (solvable in polynomial time) results, generalizing several known facts.