---
tag: 986TEMMP0H
kind: concept
name: Flag algebra
sources:
  - wikipedia: en:69378275@r1317768013
    locator: Flag algebra
    note: adopted
    mention: wikipedia://en/69378275
    sections: [Summary]
same_as:
  wikidata: Q111953946
  wikipedia: Flag algebra
inventory: [H4PN6AVXDK]
---

## Summary

**Flag algebras** are an important computational tool in the field of graph theory which have a wide range of applications in homomorphism density and related topics. Roughly, they formalize the notion of adding and multiplying homomorphism densities and set up a framework to solve [[graph homomorphism|052JJ9YVNM]] inequalities with computers by reducing them to semidefinite programming problems. Originally introduced by Alexander Razborov in a 2007 paper, the method has since come to solve numerous difficult, previously unresolved graph theoretic questions. These include the $D_{2,3}$ question regarding the region of feasible edge density, triangle density pairs and the maximum number of pentagons in triangle free graphs.