  The $k$-th power of a graph $G$ is the graph whose vertex set is $V(G)^k$,
where two distinct $k$-tuples are adjacent iff they are equal or adjacent in
$G$ in each coordinate. The Shannon capacity of $G$, $c(G)$, is
$\lim_{k\to\infty}\alpha(G^k)^{1/k}$, where $\alpha(G)$ denotes the
independence number of $G$. When $G$ is the characteristic graph of a channel
$\mathcal{C}$, $c(G)$ measures the effective alphabet size of $\mathcal{C}$ in
a zero-error protocol. A sum of channels, $\mathcal{C}=\sum_i \mathcal{C}_i$,
describes a setting when there are $t\geq 2$ senders, each with his own channel
$\mathcal{C}_i$, and each letter in a word can be selected from either of the
channels. This corresponds to a disjoint union of the characteristic graphs,
$G=\sum_i G_i$.
  We show that for any fixed $t$ and any family $F$ of subsets of
$T={1,2,...,t}$, there are $t$ graphs $G_1,G_2, ...,G_t$, so that for every
subset $I$ of $T$, the Shannon capacity of the disjoint union $\sum_{i \in I}
G_i$ is "large" if $I$ contains a member of $F$, and is "small" otherwise.
