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  "body": "\n## Summary\n\n**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.\n",
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