A 1971 conjecture of Graham (later repeated by Erdős and Graham) asserts that every set \(A \subseteq {{\mathbb F}_{p}} \; \backslash \; \{0\}\) has an ordering whose partial sums are all distinct. We prove this conjecture for sets of size \(|A| \leqslant e^{{(\log p)}^{1/4}}\) ; our result improves the previous bound of log p/log log p. One ingredient in our argument is a structure theorem involving dissociated sets, which may be of independent interest.
