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We introduce a novel approach for temporal activity segmentation with timestamp supervision. Our main contribution is a graph convolutional network, which is learned in an end-to-end manner to exploit both frame features and connections between neighboring frames to generate dense framewise labels from sparse timestamp labels. The generated dense framewise labels can then be used to train the segmentation model. In addition, we propose a framework for alternating learning of both the segmentation model and the graph convolutional model, which first initializes and then iteratively refines the learned models. Detailed experiments on four public datasets, including 50 Salads, GTEA, Breakfast, and Desktop Assembly, show that our method is superior to the multi-layer perceptron baseline, while performing on par with or better than the state of the art in temporal activity segmentation with timestamp supervision.