Graph colorings

Graph coloring is a way of assigning colors to the points (vertices) of a network so that no two connected points share the same color. Think of it like scheduling exams for students: each student is a vertex, and if they share a course (an edge), they must have a different exam time (color). The goal is to use the fewest colors possible while respecting this rule. This concept helps in solving problems related to resource allocation, pattern recognition, and network design by visually and logically categorizing connected elements without conflicts.