Constraint Satisfaction Problems (CSP) have been widely studied in several research areas like Artificial Intelligence or Operational Research due their complexity and industrial interest. From previous research areas, heuristic (informed) search methods have been particularly active looking for feasible approaches. One of the critical problems to work with CSP is related to the exponential growth of computational resources needed to solve even the simplest problems. This paper presents a new efficient CSP graph-based representation to solve CSP by using Ant Colony Optimization (ACO) algorithms. This paper presents also a new heuristic (called Oblivion Rate), that have been designed to improve the current state-of-the-art in the application of ACO algorithms on these domains. The presented graph construction provides a strong reduction in both, the number of connections and the number of nodes needed to model the CSP. Also, the new heuristic is used to reduce the number of pheromones in the system (allowing to solve problems with an increasing complexity). This new approach has been tested, as case study, using the classical N-Queens Problem. Experimental results show how the new approach works in both, reducing the complexity of the resulting CSP graph and solving problems with increasing complexity through the utilization of the Oblivion Rate.