tianxingchen/application-of-welsh-powell-algorithm-to-graph-coloring-problem

This project applies the Welsh-Powell algorithm to the classic "map coloring" problem, figuring out the minimum number of colors needed to color a map so that no two adjacent regions share the same color. The repository demonstrates this approach by coloring a map of China and includes a mathematical proof that the algorithm runs efficiently, in O(n²) time. At a high level, the algorithm works by treating each region of a map as a "node" and connections between neighboring regions as links between nodes. It then sorts all nodes by how many neighbors they have (their "degree"), starting with the most connected ones. It assigns the first color to the top node, then moves down the list giving that same color to any node that isn't adjacent to an already-colored one. Once no more nodes can take that color, it introduces a new color and repeats the process until every node is colored. The key insight is that by coloring the most connected regions first, you reduce the chance of needing extra colors later. Importantly, this greedy approach doesn't always produce the absolute minimum number of colors, but it reliably finds a good approximation. This would be useful for anyone studying graph theory, computer science students learning about algorithms, or practitioners dealing with scheduling and resource allocation problems. The classic real-world application is timetable scheduling, if you think of courses as regions and shared students or rooms as adjacency, the same algorithm can help assign time slots with minimal conflicts. The China map example in the repository serves as a concrete, visual demonstration: it successfully colors all provinces using just four colors, which the author confirms is the optimal solution. The project is straightforward and educational in nature. It provides Python code that takes an adjacency matrix as input and outputs both the color assignments and a verification that no adjacent regions conflict. The README is written in Chinese, and the implementation focuses on clarity rather than performance optimization.