Bounds for cell entries in contingency tables given marginal totals and decomposable graphs

Upper and lower bounds on cell counts in cross-classifications of nonnegati ve counts play important roles in a number of practical problems, including statistical disclosure limitation, computer tomography, mass transportatio n, cell suppression, and data swapping. Some features of the Frechet bounds are well known, intuitive, and regularly used by those working on disclosu re limitation methods, especially those for two-dimensional tables. We prev iously have described a series of results relating these bounds to theory o n loglinear models for cross-classified counts. This paper provides the act ual theory and proofs for the special case of decomposable loglinear models and their related independence graphs. It also includes an extension linke d to the structure of reducible graphs and a discussion of the relevance of other results linked to nongraphical loglinear models.