Multi-robot coordination and cooperation are critical behaviors that improve team capabilities and enable new tasks in application areas like autonomous construction, agriculture, and extended operation in large unknown regions. This dissertation examines these behaviors in the context of the multi-robot resource allocation problem, where robots must be allocated to regions of service. In particular, we are interested in uncertainty-tolerant approaches that apply to large multi-robot teams. We introduce a graph-based modeling framework for the multi-robot resource allocation problem that offers unprecedented richness in representing inter-region relationships and reward models. We first address the multi-agent coverage control problem, introducing graph-based computation via Graph Neural Networks, which boasts improved performance and scalability by leveraging learned inter-agent communication strategies. We then address the multi-robot task allocation problem in complex multi-task missions where coordination and cooperation are explicitly required. We introduce a network-flow-based planning approach that produces high quality solutions to large problems in seconds. We expand this approach into an online setting that re-plans around task failures and unexpected observations. We demonstrate empirically that these modeling approaches and algorithms bring performance improvements that further the state of the art by leveraging the fundamental graph structure present in some multi-robot problems.