Minor-Closed Families

Minor-closed families refer to collections of structures, such as graphs or matroids, that remain unchanged when you remove elements or contract certain parts. In simpler terms, if you can make a new structure by deleting some elements or merging others, and that new structure still belongs to the same family, then that family is minor-closed. This concept is important in fields like graph theory and combinatorics because it helps mathematicians understand the properties and limitations of different structures, aiding in the development of theories around them, like the famous Graph Minor Theorem.