In this paper, some new criteria for detecting whether a finite game is potential are proposed by solving potential equations. The verification equations with the minimal number for checking a potential game are obtained for the first time. Compared with the existing results, a reduced-complexity testing condition is derived. Some connections between the potential equations and the existing characterizations of potential games are established. It is revealed that a finite game is potential if and only if its every bimatrix sub-game is potential. (C) 2016 Elsevier Ltd. All rights reserved.