The Four Color Theorem: A Constructive Proof and a Coloring Algorithm

In this version, the proof has become shorter and, in our view, clearer. The proof is now based on a single mechanism — the forced chain. K₄ and odd stars are treated as special cases of this mechanism. A demonstration of the algorithm has also been added, showing how it sequentially finds forced chains, splits edges, and arrives at a 4-coloring.