Graham's conjecture on valid orderings in cyclic groups of prime order

Let $p$ be a prime, and let $A\subseteq\mathbb{Z}_p\setminus\{0\}$. An ordering $a_1,\ldots,a_{|A|}$ of $A$ is valid if its partial sums

$$p_i=a_1+\cdots+a_i\qquad(1\leq i\leq |A|)$$

are pairwise distinct. Graham's conjecture. Every subset $A\subseteq\mathbb{Z}_p\setminus\{0\}$ has a valid ordering. The conjecture was recently proved for sufficiently large primes by Pham and Sauermann, but remains open for general abelian groups, including the cyclic case in general; the paper improves the best known bound for subsets of $\mathbb{Z}_k\setminus\{0\}$ for which the corresponding ordering is guaranteed.