A maximal clique is a clique that cannot be extended by including one more adjacent vertex, meaning it is not a subset of a larger clique. A maximum clique (i.e., clique of largest size in a given graph) is therefore always maximal, but the converse does not hold. Maximal cliques are important in graph theoretic applications, including graph coloring and fractional graph coloring.

Bron-Kerbosch algorithm | clique | clique covering | clique covering number | clique polynomial | lower clique number | maximal clique polynomial | maximal independent vertex set | maximal set | maximum clique