  The index coding problem is a problem of efficient broadcasting with
side-information. We look at the uniprior index coding problem, in which the
receivers have disjoint side-information symbols and arbitrary demand sets.
Previous work has addressed single uniprior index coding, in which each
receiver has a single unique side-information symbol. Modeling the uniprior
index coding problem as a \textit{supergraph}, we focus on a class of uniprior
problems defined on \textit{generalized cycle} supergraphs. For such problems,
we prove upper and lower bounds on the optimal broadcast rate. Using a
connection with Eulerian directed graphs, we also show that the upper and lower
bounds are equal for a subclass of uniprior problems. We show the NP-hardness
of finding the lower bound for uniprior problems on generalized cycles.
Finally, we look at a simple extension of the generalized cycle uniprior class
for which we give bounds on the optimal rate and show an explicit scheme which
achieves the upper bound.
