Feat graph colouring

[Prathameshk2024]

• Assigns colors to graph vertices ensuring no adjacent vertices share the same color • Uses backtracking approach for optimal solution • Finds chromatic number (minimum colors needed) • Implements greedy coloring for faster approximation • Includes Welsh-Powell algorithm (degree-based ordering) • Validates coloring solutions for correctness • Demonstrates with multiple test cases (triangle, Petersen, bipartite, random graphs) • Time complexity: O(m^V), Space complexity: O(V) • Production-ready implementation with comprehensive examples