In this work, we address the problem of multi-domain image-to-image translation with particular attention paid to computational cost. In particular, current state of the art models require a large and deep model in order to handle the visual diversity of multiple domains. In a context of limited computational resources, increasing the network size may not be possible. Therefore, we propose to increase the network capacity by using an adaptive graph structure. At inference time, the network estimates its own graph by selecting specific sub-networks. Sub-network selection is implemented using Gumbel-Softmax in order to allow end-to-end training. This approach leads to an adjustable increase in number of parameters while preserving an almost constant computational cost. Our evaluation on two publicly available datasets of facial and painting images shows that our adaptive strategy generates better images with fewer artifacts than literature methods