  Round-based models are very common message-passing models; combinatorial
topology applied to distributed computing provides sweeping results like
general lower bounds. We combine both to study the computability of k-set
agreement. Among all the possible round-based models, we consider oblivious
ones, where the constraints are given only round per round by a set of allowed
graphs. And among oblivious models, we focus on closed-above ones, that is
models where the set of possible graphs contains all graphs with more edges
than some starting graphs. These capture intuitively the underlying structure
required by some communication model, like containing a ring. We then derive
lower bounds and upper bounds in one round for k-set agreement, such that these
bounds are proved using combinatorial topology but stated only in terms of
graph properties. These bounds extend to multiple rounds when limiting our
algorithms to be oblivious -- recalling only pairs of processes and initial
value, not who send what and when.
