$D$.

A packet is successfully transmitted from the transmitting relay $R_t$ to the destination $D$ if the Signal-to-Noise Ratio (SNR), denoted by $\text{SNR}_{R_t D}$, is greater than or equal to the capture ratio $\gamma_0$, i.e., $$\begin{aligned}
\label{eq:SNR_RD}
\frac{g_{R_t D}P_{R_t}}{n_D} \geq  \gamma_0 \; , \quad R_t\in\mathcal{T}, R_t \neq R_r \; .\end{aligned}$$ A packet is successfully transmitted from source $S$ to the receiving relay $R_r$, if the Signal-to-Interference-and-Noise Ratio (SINR) at the receiving relay, denoted by $\text{SINR}_{S R_r}$ is greater than or equal to $\gamma_0$, i.e., $$\begin{aligned}
\label{eq:SNR_SR}
\frac{g_{S R_r}P_{S}}{g_{R_t R_r} P_{R_t} \mathbb{I}(R_t R_r)  +  n_{R_r}} \geq  \gamma_0 \; , \quad R_r\in\mathcal{C}, R_r \neq R_t \; ,\end{aligned}$$ where $ \mathbb{I}(R_t R_r)$ is a factor indicating whether interference cancellation is satisfied and it is described by $$\begin{aligned}
\label{eq:index}
\mathbb{I}(R_t R_r) = 
\begin{cases} 
0 , & \text{if } \displaystyle \frac{g_{R_t R_r} P_{R_t}}{g_{S R_r}P_{S} +  n_{R_r}} \geq  \gamma_0 \; ,   \\
1 , &\text{otherwise.}
\end{cases}\end{aligned}$$

The following proposition states that if the maximum powers $P_{S}^{\max}$ and $P_{R_t}^{\max}$ are large enough (thus not imposing any limitations/constraints), for each pair of relays $R_r$ and $R_t$, then we can always find power levels such that interference cancellation conditions are satisfied.

\[prop:1\] Let $P_{S}^{\max}=\infty$ and $P_{R_t}^{\max}=\infty$. For each pair 