Approximating maximum independent sets by excluding subgraphs

An approximation algorithm for the maximum independent set problem is given, improving the best performance guarantee known to \({\cal O}\)(n/(log n)2). We also obtain the same performance guarantee for graph coloring. The results can be combined into a surprisingly strong simultaneous performance guarantee for the clique and coloring problems.

[1]  Avrim Blum,et al.  An O(n0.4)-approximation algorithm for 3-coloring , 1989, STOC '89.

[2]  Piotr Berman,et al.  On the Complexity of Approximating the Independent Set Problem , 1989, Inf. Comput..

[3]  Vasek Chvátal,et al.  Determining the Stability Number of a Graph , 1976, SIAM J. Comput..

[4]  Avi Wigderson,et al.  Improving the performance guarantee for approximate graph coloring , 1983, JACM.

[5]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[6]  L. Lovász,et al.  Geometric Algorithms and Combinatorial Optimization , 1981 .

[7]  James B. Shearer,et al.  A note on the independence number of triangle-free graphs , 1983, Discret. Math..

[8]  Avrim Blum,et al.  Some tools for approximate 3-coloring , 1990, Proceedings [1990] 31st Annual Symposium on Foundations of Computer Science.

[9]  Nathan Linial,et al.  Graph products and chromatic numbers , 1989, 30th Annual Symposium on Foundations of Computer Science.

[10]  P. Erdős.  Some remarks on chromatic graphs , 1967 .

[11]  László Lovász,et al.  On the Shannon capacity of a graph , 1979, IEEE Trans. Inf. Theory.

[12]  János Komlós,et al.  A Note on Ramsey Numbers , 1980, J. Comb. Theory, Ser. A.

[13]  David S. Johnson,et al.  Approximation algorithms for combinatorial problems , 1973, STOC.