Methods for vertex coloring

When solving the graph vertex coloring problem, we aim to color the vertices of a graph using the smallest possible number of colors while ensuring that no two adjacent vertices share the same color. This problem has applications in various fields, such as scheduling, resource allocation, and network optimization. Its solutions range from exact methods to various simple heuristics and metaheuristics, depending on the size and complexity of the graph. The goal is to provide a brief overview of these methods and to describe and implement selected approaches in more detail.