The optimal controlled islanding of power systems is a practical solution to prevent system blackouts if the boundary of islands and corrective control actions in each island are carefully specified. This paper establishes a model for the controlled islanding problem by a proposed mixed integer linear program (MILP). The frequency-arresting (FA) and frequency-stabilising (FS) constraints are linearised and incorporated in our FA-FS-constrained MILP model to prevent triggering of load shedding (LS) relays. This achievement makes our model capable of handling low-inertia networks. Intentional LS and stepwise generation curtailment are corrective actions accommodated for frequency control and power mismatch considerations. These corrective actions increase the degree of freedom and broaden the feasible space of the MILP model under the envisaged tough operating conditions. Our model's computational efficiency is improved using a proposed graph theory-based network reduction technique. The basic groups of coherent generators, determined in the offline mode, are aggregated as equivalent buses using an extended Steiner tree method. A graph-path determination technique is also proposed to generate disconnection constraints (between equivalent buses of incoherent areas) and bus-allocation constraints. Simulation results on the IEEE 39-bus test system and a 76-bus case study verify the proposed network reduction technique's effectiveness and the MILP model.