In [@GunduzYenerGoldsmithPoor] and [@OngKellettJohnson], the multi-cast setting of the multi-way relay channel was considered, where each node has one message intended to all other nodes. In that case, it was shown that the cut-set bounds are sufficient to obtain an asymptotic characterization of the sum-capacity. Interestingly however, in our broadcast setting this is not the case. We can notice that the bound of Corollary \[Corollary:CutSetBounds\], which is based on the cut-set bounds in Theorem \[CutSetBounds\], provides a sum-capacity upper bound of the form $$\begin{aligned}
C_g\leq\frac{3}{2}\log(P)+o(\log(P)).\end{aligned}$$ Thus, this corollary gives a sum-capacity upper bound with a pre-log of 3/2. The reason behind this is that Theorems \[CutSetBounds\] and \[BCBounds\] bound the sum of two rates by $\frac{1}{2}\log(P)+o(\log(P))$. Next, we develop more upper bounds, and show that the Y-channel has a sum-capacity pre-log of 1, $$\begin{aligned}
C_g\leq\log(P)+o(\log(P)).\end{aligned}$$ This means that, while the bound in Corollary \[Corollary:CutSetBounds\] might be useful at lower $P$, it can not give a tight sum-capacity upper bound as $P$ increases. Thus, contrary to the multi-cast setting, the cut-set bounds are not sufficient in the broadcast setting and more bounds are required for an asymptotic characterization of the sum-capacity. A bounds with a capacity pre-log of 1 is given 