Reachability of marked graphs with token capacity constraints is generalized to that with respect to any subgraph of the marked graph. It is shown that submarking reachability is equivalent to the existence of a minimum firing count vector satisfying a set of equality and inequality constraints. A necessary and sufficient condition is presented for the existence of the minimum firing count vector together with its constructing algorithm. The result can be applied in finding the firing sequence of minimum length in practical sequential control problems.