Common graph

Concept in extremal graph theory

In graph theory, an area of mathematics, common graphs belong to a branch of extremal graph theory concerning inequalities in homomorphism densities. Roughly speaking, is a common graph if it "commonly" appears as a subgraph, in a sense that the total number of copies of in any graph and its complement is a large fraction of all possible copies of on the same vertices. Intuitively, if contains few copies of , then its complement must contain lots of copies of in order to compensate for it.

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