The main focus of this paper is the presentation of reliable methods for the determination of the optimum coloring of a graph, commonly known in the literature as vertex coloring problem. It has been shown that networks of capacitively coupled oscillators can be used to solve vertex coloring problems. In this paper we address the negative impact of an unbalanced number of couplings for the oscillators on the performance of the network and compensate for this non-uniform coupling structure by an adjustment in the network itself. The negative effect of the memristor device-to-device variability of the NbOx memristor on the array functionality will be investigated and reduced via an adaptation of the memristor operating point. The main improvement in network performance is achieved by setting up a control procedure allowing the network to bypass the local solutions and converge to the global one. Two strategies inspired by global optimization algorithms will be proposed to allow the network to overcome sub-optimal solutions, and find the solution corresponding to the absolute minimum of a performance measure function of the vertex coloring problem.