linguistic:paraphrasing, information:highlighting
Mathematics

Mathematical results concerning cliques include the following.

Several important classes of graphs may be defined or characterized by their cliques:

Additionally, many other mathematical constructions involve cliques in graphs. Among them,

Closely related concepts to complete subgraphs are subdivisions of complete graphs and complete graph minors. In particular, Kuratowski's theorem and Wagner's theorem characterize planar graphs by forbidden complete and complete bipartite subdivisions and minors, respectively.