A system of asynchronous parallel processes is represented by an exclusion graph in which a vertex is a process and an edge is a pair of mutually excluding processes. The mutual exclusion problem can be managed by simple entrance and exit protocols using PVchunk operations on a single shared variable when the graph is a threshold one. Ordman wonders if an efficient way exists for managing mutual exclusion situations modeled by more complex graphs than the threshold ones. A start is made on that here: we present a solution of the problem when the model is in the class of matrogenic graphs, which properly contains the threshold graphs.