Graph minors

Graph minors are a concept in graph theory, which is the study of connected structures made up of points (vertices) and lines (edges). A graph minor is formed by taking a larger graph and performing certain operations: removing vertices and edges, or contracting edges (which merges the two vertices at either end into one). The idea is useful in understanding the properties of graphs, as many complex problems can be resolved by identifying whether a smaller, simpler graph configuration (the minor) exists within a larger one. This concept helps in areas like network design and algorithm efficiency.