Lower bounds on the stability number of graphs computed in terms of degrees
Discrete Mathematics
A probabilistic lower bound on the independence number of graphs
Discrete Mathematics
Polynomially solvable cases for the maximum stable set problem
Discrete Applied Mathematics - Special volume: Aridam VI and VII, Rutcor, New Brunswick, NJ, USA (1991 and 1992)
Approximation algorithms for NP-hard problems
A lower bound on the independence number of a graph
Discrete Mathematics
On vertex orderings and the stability number in triangle-free graphs
Discrete Mathematics - Special issue on the 17th british combinatorial conference selected papers
On the independence number of a graph in terms or order and size
Discrete Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Maximum Edge-Disjoint Paths Problem in Bidirected Trees
SIAM Journal on Discrete Mathematics
Forbidden subgraphs implying the MIN-algorithm gives a maximum independent set
Discrete Mathematics
A note on greedy algorithms for the maximum weighted independent set problem
Discrete Applied Mathematics
Approximations of Independent Sets in Graphs
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
Approximating an Interval Scheduling Problem
APPROX '98 Proceedings of the International Workshop on Approximation Algorithms for Combinatorial Optimization
An Optimisation Algorithm for Maximum Independent Set with Applications in Map Labelling
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Measure and conquer: a simple O(20.288n) independent set algorithm
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Partitions of graphs into small and large sets
Discrete Applied Mathematics
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A maximum independent set problem for a simple graph G = (V, E) is to find the largest subset of pairwise nonadjacent vertices. The problem is known to be NP-hard and it is also hard to approximate. Within this article we introduce a non-negative integer valued function p defined on the vertex set V (G) and called a potential function of a graph G, while P(G) = maxv∈V(G) p(v) is called a potential of G. For any graph P(G) ≤ Δ(G), where Δ(G) is the maximum degree of G. Moreover, Δ(G) - P(G) may be arbitrarily large. A potential of a vertex lets us get a closer insight into the properties of its neighborhood which leads to the definition of the family of GreedyMAX-type algorithms having the classical GreedyMAX algorithm as their origin. We establish a lower bound 1/(P + 1) for the performance ratio of GreedyMAX-type algorithms which favorably compares with the bound 1/(Δ + 1) known to hold for GreedyMAX. The cardinality of an independent set generated by any GreedyMAX-type algorithm is at least Σv∈V(G)(p(v)+1)-1, which strengthens the bounds of Turáan and Caro-Wei stated in terms of vertex degrees.