On the Maximum Number of Cliques in a Graph

A clique is a set of pairwise adjacent vertices in a graph. We determine the maximum number of cliques in a graph for the following graph classes: (1) graphs with n vertices and m edges; (2) graphs with n vertices, m edges, and maximum degree ∆; (3) d-degenerate graphs with n vertices and m edges; (4) planar graphs with n vertices and m edges; and (5) graphs with n vertices and no K5-minor or no K3,3-minor. For example, the maximum number of cliques in a planar graph with n vertices is 8(n − 2). Keywords. extremalgraphtheory,Turán’sTheorem,clique,Completesubgraph,Degeneracy, Graph minor, Planar graph, K5-minor, K3,3-minor.

• Type: Journal
• Year: 2007
• Where: GC
• Authors: David R. Wood
• Keywords: Adjacent Vertices, Applied Computing, Clique, GC 2007, Maximum Number