Analysis of the impact of the number of edges in connected graphs on the computational complexity of the independent set problem

Under study is the complexity status of the independent set problem in a class of connected graphs that are defined by functional constraints on the number of edges depending on the number of vertices. For every natural number C , this problem is shown to be polynomially solvable in the class of gra...

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Bibliographic Details
Published in:Journal of applied and industrial mathematics Vol. 6; no. 1; pp. 97 - 99
Main Author: Malyshev, D. S.
Format: Journal Article
Language:English
Published: Dordrecht SP MAIK Nauka/Interperiodica 01.01.2012
Springer Nature B.V
Subjects:
Algorithms
Complexity
Computation
Computational mathematics
Exponents
Graphs
Intersections
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Set theory
Studies
computational complexity
independent set problem
ISSN:1990-4789, 1990-4797
Online Access:Get full text
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Summary:Under study is the complexity status of the independent set problem in a class of connected graphs that are defined by functional constraints on the number of edges depending on the number of vertices. For every natural number C , this problem is shown to be polynomially solvable in the class of graphs On the other hand, this problem is proved to be not polynomially solvable in the class of graphs for every unbounded nondecreasing function f ( n ): ℕ → ℕ, such that exponent of this function grows faster than a polynomial function of n . The latter result is true if there does not exist a subexponential algorithm for solving the independent set problem.
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ISSN:1990-4789
1990-4797
DOI:10.1134/S1990478912010103