A member of a collection of sets is said to be maximal if it cannot be expanded to another member by addition of any element. Maximal sets are important in graph theory since many graph theoretic algorithms require only maximal sets of edge and vertex collections and the numbers of maximal sets are typically much smaller than the total numbers of sets in a graph.

maximal clique | maximal element | maximal independent edge set | maximal independent vertex set | maximal irredundant set