Improving the Performance of Graph Coloring Algorithms through Backtracking

Introduction Imagine trying to schedule multiple classes at a school so that no two classes sharing the same teacher happen at the same time. Or assigning frequencies to cell towers so that no neighboring towers interfere. This is where Graph Colouring comes in—a classic but notoriously difficult problem in computer science. What is Graph Colouring? At its core, graph colouring involves assigning colors to the vertices of a graph such that no two adjacent vertices share the same color . A vertex  is like a point or node. An    edge connects two vertices. A valid coloring  means adjacent vertices get different colors. The chromatic number  is the minimum number of colors needed to achieve this. Classic Backtracking: The Smart Brute Force The traditional way to tackle graph colouring is through backtracking . It’s a recursive method where you assign colors to one vertex at a time. If you hit a conflict (i.e., no valid color is left for a vertex), you...