This three-year award for U.S.-France cooperative research in mathematics involves Robin Thomas of Georgia Institute of Technology, Paul Seymour of Princeton University, G. Neil Robertson of Ohio State University and the research group of Bruce Reed of the University of Paris VI. The award provides travel support and living expenses to the three U.S. researchers. They intend to develop a theory of digraph minors with particular emphasis on tree decompositions. This theory will be analogous to graph minor theory which has led to efficient algorithms. The project takes advantage of French expertise in graph minor theory and will contribute towards a new structural theory.