The forcing conjecture for graphs

A graph is called forcing if it is $p$-forcing for every $0<p<1$, where a graph $H$ is $p$-forcing when, for every graph sequence of edge density tending to $p$, the condition $t_H(G_n)=(1+o(1))p^{|E(H)|}$ together with the corresponding condition for $K_2$ implies quasirandomness with density $p$. Forcing conjecture. A graph $H$ is forcing if and only if it is bipartite and contains a cycle. Bipartiteness and the presence of a cycle are necessary conditions; the conjecture proposes that they are also sufficient. The source proves the assertion for bipartite graphs having two vertices in one part complete to the other part, with that part containing at least two vertices, but leaves the general characterization open.