We consider clustering in the perturbation resilience model that has been studied since the work of Bilu and Linial  and Awasthi, Blum and Sheffet . A clustering instance I is said to be α-perturbation resilient if the optimal solution does not change when the pairwise distances are modified by a factor of α and the perturbed distances satisfy the metric property-this is the metric perturbation resilience property introduced in  and a weaker requirement than prior models. We make two high-level contributions. We show that the natural LP relaxation of κ-center and asymmetric κ-center is integral for 2-perturbation resilient instances. We belive that demonstrating the goodness of standard LP relaxations complements existing results [12, 4] that are based on new algorithms designed for the perturbation model. We define a simple new model of perturbation resilience for clustering with outliers. Using this model we show that the unified MST and dynamic programming based algorithm proposed in  exactly solves the clustering with outliers problem for several common center based objectives (like κ-center, κ-means, κ-median) when the instances is 2-perturbation resilient. We further show that a natural LP relxation is integral for 2-perturbation resilient instances of κ-center with outliers.