Approach to proving the Four Color Theorem

Abstract: This paper proposes a novel approach to proving the Four Color Theorem, distinct from the traditional "reducible configurations" method. By introducing concepts such as "outer boundary", "primitive set", "Properties A/B/C", and the operation of "adding an n-point region on an interval", we construct a step-by-step framework for coloring any given planar graph. The core of this framework consists of four theorems, which ensure that after sequentially adding specific regions to an outer boundary satisfying Properties A, B, and C, the new outer boundary continues to satisfy these properties, ultimately allowing the entire graph to be colored using only four colors. This method avoids computer enumeration and offers a more constructive perspective on the proof.