Autoregressive transformer training through next-token prediction has driven remarkable advances in language modeling and has become increasingly effective for time-series modeling. Yet its success in temporal graph learning remains limited, and most temporal link-prediction methods are discriminative rather than autoregressive. While temporal graphs can have a natural serialization through chronological ordering edges, they lack an obvious graph-independent tokenization: existing node tokenization often uses a vocabulary that grows with the number of nodes, limiting scalability and cross-graph training. We propose GTGT, Generative Temporal Graph Transformer, a simple yet powerful vocabulary-free framework for self-supervised next-event prediction on temporal graphs. It predicts events for observed destinations, behavioral descriptors for novel destinations, and time gaps before new event. These targets have shared meanings across graphs, allowing one transformer to train across disjoint node sets without node-specific learned parameters. Local node identifiers let attention capture graph structure: Theoretically, we can show that our transformer-based model has the capacity for time-respecting message passing mechanisms. On Temporal Graph Benchmark (TGB), our GTGT not only achieves comparable or better link-prediction performance than established baselines, but also has much lower training cost. These results open the door to temporal graph pretraining for forecasting and other downstream tasks, providing a concrete step toward temporal graph foundation models.

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