Matching, Euler tours and the Chinese postman

The solution of the Chinese postman problem using matching theory is given. The convex hull of integer solutions is described as a linear programming polyhedron. This polyhedron is used to show that a good algorithm gives an optimum solution. The algorithm is a specialization of the more general b-matching blossom algorithm. Algorithms for finding Euler tours and related problems are also discussed. © 1973 The Mathematical Programming Society.