While serializability always guarantees application correctness, lower isolation levels can be chosen to improve transaction throughput at the risk of introducing certain anomalies. A set of transactions is robust against a given isolation level if every possible interleaving of the transactions under the specified isolation level is serializable. Robustness therefore always guarantees application correctness with the performance benefit of the lower isolation level. While the robustness problem has received considerable attention in the literature, only sufficient conditions have been obtained. The most notable exception is the seminal work by Fekete where he obtained a characterization for deciding robustness against SNAPSHOT ISOLATION. In this article, we address the robustness problem for the lower SQL isolation levels READ UNCOMMITTED and READ COMMITTED, which are defined in terms of the forbidden dirty write and dirty read patterns. The first main contribution of this article is that we characterize robustness against both isolation levels in terms of the absence of counter-example schedules of a specific form (split and multi-split schedules) and by the absence of cycles in interference graphs that satisfy various properties. A critical difference with Fekete's work, is that the properties of cycles obtained in this article have to take the relative ordering of operations within transactions into account as READ UNCOMMITTED and READ COMMITTED do not satisfy the atomic visibility requirement. A particular consequence is that the latter renders the robustness problem against READ COMMITTED coNP-complete. The second main contribution of this article is the coNP-hardness proof. For READ UNCOMMITTED, we obtain LOGSPACE-completeness.