We examine several families of constraint systems. Constraint satisfaction and network stability are well understood; network stability was introduced in an attempt to understand the role of fanout. We introduce two new families of constraint systems, in a new attempt to limit fanout. These two families are graph constraint satisfaction and bipartite constraint satisfaction. We obtain the following results: (1) an extension of Schaefer's classification argument for boolean satisfiability to boolean graph constraint satisfaction and bipartite constraint satisfaction, (2) a characterization of the graph constraint satisfaction problems that lack fanout in terms of a new problem, the generalized matroid parity problem, which gives rise to many new problems whose complexity is yet to be determined; in particular, the coindependent set problem is shown to be polynomial, and (3) generalized matroid intersection characterizes the lack of fanout in the bipartite case, with a family of matroid intersection problems as a special polynomially solvable subcase.