Common graph

Summary

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