Improved Approximations for Weighted and Unweighted Graph Problems

We obtain improved approximation ratios for problems of a broad class called weighted hereditary induced-subgraph maximization problems, in particular for the maximum independent set, maximum clique and maximum ℓ-colorable induced subgraph, as well as for the minimum coloring problem. We also study the minimum chromatic sum and show that its weighted version polynomially reduces to the weighted independent set problem in such a way that approximation ratios are preserved (up to a multiplicative constant).