While many approaches exist to segment retinal vessels in fundus photographs, only a limited number focus on the construction and disambiguation of arterial and venous trees. Previous approaches are local and/or greedy in nature, making them susceptible to errors or limiting their applicability to large vessels. We propose a more global framework to generate arteriovenous trees in retinal images, given a vessel segmentation. In particular, our approach consists of three stages. The first stage is to generate an overconnected vessel network, named the vessel potential connectivity map (VPCM), consisting of vessel segments and the potential connectivity between them. The second stage is to disambiguate the VPCM into multiple anatomical trees, using a graph-based metaheuristic algorithm. The third stage is to classify these trees into arterial or venous (A/V) trees. We evaluated our approach with a ground truth built based on a public database, showing a pixel-wise classification accuracy of 88.15% using a manual vessel segmentation as input, and 86.11% using an automatic vessel segmentation as input.