  We study forcing pairs for quasirandom graphs. Chung, Graham, and Wilson
initiated the study of families $\\mathcal F$ of graphs with the property that
if a large graph $G$ has approximately homomorphism density $p^{e(F)}$ for some
fixed $p\in(0,1]$ for every $F\in \mathcal F$, then $G$ is quasirandom with
density $p$. Such families $\mathcal F$ are said to be forcing. Several forcing
families were found over the last three decades and characterising all
bipartite graphs $F$ such that $(K_2,F)$ is a forcing pair is a well-known open
problem in the area of quasirandom graphs, which is closely related to
Sidorenko's conjecture. In fact, most of the known forcing families involve
bipartite graphs only.
  We consider forcing pairs containing the triangle $K_3$. In particular, we
show that if $(K_2,F)$ is a forcing pair, then so is $(K_3,F')$, where $F'$ is
obtained from $F$ by replacing every edge of $F$ by a triangle (each of which
introduces a new vertex). For the proof we first show that $(K_3,C'_4)$ is a
forcing pair, which strengthens related results of Simonovits and S\'os and of
Conlon et al.
