This is a 36 month award proposed by Dr. Michael Plummer, Vanderbilt University, collaborating with Dr. Nawarat Ananchuen, Silpakorn University in Thailand. Dr. Plummer requests funds for travel and 30 days per diem per year for two years to carry out a cooperative project on matching extension in graphs and networks. Dr. Plummer is a world leader in graph theory and highly respected in this field. This proposal is well written, with nice general outlines of the problems. This study is likely to result in significant contributions to this field. This cooperative project is between a world class expert and a junior colleague in Thailand, and, if successful, could stimulate further research in graph theory in East Asia.