The deployment of edge servers make a significant impact on the service quality of a Mobile Edge Computing (MEC) system. This service quality relies on solving two key sub-problems: 1) interference management between servers 2) the placement of MEC servers. To improve the Quality of Service (QoS), we propose a method based on Graph Partition (GP) and Upper Confidence Bound (UCB) for solving these two sub-problems. Regarding interference management, we use an undirected graph to represent the interference between MEC servers so that the overall graph can be divided into multiple subsets of non-interfering MEC servers. Regarding server placement, we propose a Multiple Choice-Upper Confidence Bound (MC-UCB) algorithm that place an collection of interference aware edge servers in each selection. To evaluate the performance, we define a user's QoS function based on transmission delay, throughput, and user density comprehensively and compared with Particle Swarm Optimization (PSO) and Genetic Algorithm (GA) from previous work. The simulation results show that the performance of the proposed algorithms is improved by more than 4% compared with the GA algorithm and 6% compared with the PSO algorithm.