2n\}$ in which both $\{1,\ldots, n\}$ and $\{n+1,\ldots, 2n\}$ are oriented according to $\mathcal{T}(n,1/2)$ and each pair $\{i,j\}$ with $1 \leq i \leq n, n+1 \le j \le 2n$ appears as $\overrightarrow {ij}$ with probability $\alpha$, with all choices made independently. We denote by $\mathcal{T}_{bip}$ the collection of all distributions ${\cal T}(n,n,\alpha )$ as $\alpha$ varies.

Loosely speaking a graph $H$ is [$\mathcal{T}_{bip}$-forcing]{} if no ${\cal T}(n,n,\alpha )$ shows that $H$ is not locally forcing. I.e. if there is no $\alpha \neq 1/2$ such that ${\cal T}(n,n,\alpha )$, which is not quasirandom, has the same local counts of $H$ as ${\cal T}(n,n,1/2)={\cal T}(2n,1/2)$.

Both properties [$\mathcal{T}_{cliq}$-forcing]{} and [$\mathcal{T}_{bip}$-forcing]{} can be expressed in terms of certain polynomial equations depending on the graph $H$. Our actual definitions of both properties go directly via these polynomial equations and we refer the reader to Section \[sec: counting polynomial\] for exact definitions.

Quite remarkably it turns out that if $H$ is not locally forcing one must be able to find an $\alpha$ such that either ${\cal T}(n,\alpha )$ or ${\cal T}(n,n,\alpha )$ show $H$ is not locally forcing. In particular, we show:

\[thm:-simple and esimple iff locally forcing\] $H$ is locally forcing if and only 