Density functional theory calculations are performed on 38 and 79 metal atom truncated octahedron clusters to study oxygen dissociation as a model for the initial stage of the oxygen reduction reaction. Pure platinum and alloyed platinum-titanium core-shell systems are investigated. It is found that barrierless oxygen dissociation occurs on the (111) facet of the pure platinum clusters. A barrier of ~0.3 eV is observed on the (100) facet. For the alloyed cluster, dissociation barriers are found on both facets, typically ~0.6 eV. The differences between the two systems are attributed to the ability of oxygen to distort the (111) surface of the pure platinum clusters. We show that flexibility of the platinum shell is crucial in promotion of fast oxygen dissociation. However, the titanium core stabilises the platinum shell upon alloying, resulting in a less easily distortable surface. Therefore, whilst an alloyed platinum-titanium electrocatalyst has certain advantages over the pure platinum electrocatalyst, we suggest alloying with a more weakly interacting metal will be beneficial for facilitating oxygen dissociation.