Crystal structure prediction algorithms have become powerful tools for materials discovery in recent years, however, they are usually limited to relatively small systems. The main challenge is that the number of local minima grows exponentially with the system size. In this work, we proposed two crossover-mutation schemes based on graph theory to accelerate the evolutionary structure searching by automatic decomposition methods. These schemes can detect molecules or clusters inside periodic networks using quotient graphs for crystals, and the decomposition can dramatically reduce the searching space. Sufficient examples for test, including the high-pressure phases of methane, ammonia, MgAl2O4 and boron, show that these new evolution schemes can significantly improve the success rate and searching efficiency compared with the standard method in both isolated and extended systems.