Minor-closed properties

Minor-closed properties are properties of graphs that remain true when you perform certain operations called "taking minors." A graph minor is formed by removing edges or vertices and by "contracting" edges, which combines two vertices into one. If a graph has a particular property, and that property still holds after any of these operations, then the property is called minor-closed. For example, planarity (being able to draw a graph without crossings) is minor-closed because any minor of a planar graph is also planar. These properties are important in graph theory because they help characterize and classify complex graph families.