This paper proposes a new concept, the Admissible Gap (AG), for reactive collision avoidance. A gap is called admissible if it is possible to find a collision-free motion control that guides a robot through it, while respecting the vehicle constraints. By utilizing this concept, a new navigation approach was developed, achieving an outstanding performance in unknown dense environments. Unlike the widely used gap-based methods, our approach directly accounts for the exact shape and kinematics, rather than finding a direction solution and turning it later into a collision-free admissible motion. The key idea is to analyze the structure of obstacles and virtually locate an admissible gap, once traversed, the robot makes progress towards the goal. For this purpose, we introduce a strategy of traversing gaps that respect the kinematic constraints and provides a compromise between path length and motion safety. We also propose a new methodology for extracting gaps that eliminates useless ones, thus reducing oscillations. Experimental results along with performance evaluation demonstrate the outstanding behavior of the proposed AG approach. Furthermore, a comparison with existing state-of-the-art methods shows that the AG approach achieves the best results in terms of efficiency, robustness, safety, and smoothness.