  In this note we prove two extensions of a recent combinatorial
characterization due to Li, Qiao, Wigderson, Wigderson and Zhang
(arXiv:2206.04815) of the maximal dimension of bounded rank subspaces of the
graphical matrix space associated with a bipartite graph. Our first result
shows that the above characterization remains valid for a wide class of
generalized rank functions, including e.g. the permanental rank. Our second
result extends the characterization to bounded rank subspaces of the graphical
alternating matrix space associated with a general graph.
