In abstractive summarisation, summaries can include novel sentences that are generated automatically. In order to improve the grammaticality of the generated sentences, we model a global (sentence) level syntactic structure. We couch statistical sentence generation as a spanning tree problem in order to search for the best dependency tree spanning a set of chosen words. We also introduce a new search algorithm for this task that models argument satisfaction to improve the linguistic validity of the generated tree. We treat the allocation of modifiers to heads as a weighted bipartite graph matching problem (also known as the assignment problem), a well studied problem in graph theory. Using BLEU to measure performance on a string regeneration task, we demonstrate an improvement over standard language model baselines, illustrating the benefit of the spanning tree approach incorporating an argument satisfaction model.