Flag complex

In mathematics flags certain simplicial complexes, which play a role in graph theory, geometric topology and geometric group theory.

Definition

A flag complex is an abstract simplicial complex satisfying the following condition ( " Gromov 's no- condition" ) is satisfied: if a set of vertices, such that any two vertices of belong to a common simplex, then form the vertices of a simplex.

Examples

A graph is a flag complex if and only if the following holds. This refers to the length of a shortest circuit in.

Heawood graph:

McGee graph

Tutte - Coxeter graph

• Geometric topology
• Graph Theory