  A graph $\mathcal{G}$ is referred to as $\mathsf{S}^1$-synchronizing if,
roughly speaking, the Kuramoto-like model whose interaction topology is given
by $\mathcal{G}$ synchronizes almost globally. The Kuramoto model evolves on
the unit circle, \ie the $1$-sphere $\mathsf{S}^1$. This paper concerns
generalizations of the Kuramoto-like model and the concept of synchronizing
graphs on the Stiefel manifold $\mathsf{St}(p,n)$. Previous work on state-space
oscillators have largely been influenced by results and techniques that pertain
to the $\mathsf{S}^1$-case. It has recently been shown that all connected
graphs are $\mathsf{S}^n$-synchronizing for all $n\geq2$. The previous point of
departure may thus have been overly conservative. The $n$-sphere is a special
case of the Stiefel manifold, namely $\mathsf{St}(1,n+1)$. As such, it is
natural to ask for the extent to which the results on $\mathsf{S}^{n}$ can be
extended to the Stiefel manifold. This paper shows that all connected graphs
are $\mathsf{St}(p,n)$-synchronizing provided the pair $(p,n)$ satisfies $p\leq
\tfrac{2n}{3}-1$.
