邮递员问题（也称邮路问题，Route Inspection Problem，或中国邮路问题,China Route Inspection Problem，或中国邮递员问题Chinese Postman Problem）是一个图论问题。此问题为在一个连通的无向图中找到一最短的封闭路径，且此路径需通过所有边至少一次。

简单来说，邮递员问题就是在一个已知的地区，邮差要设法找到一条最短路径，可以走过此地区所有的街道，且最后要回到出发点，

此问题是图遍历问题的一种。无向图的中国邮路问题是容易解决的，是P问题；而有向图的中国邮路问题是NP完全问题。中国邮递员问题由管梅谷教授在1960年提出，而美国国家标准和技术研究院（NIST）的 Alan Goldman 首先将此问题命名为中国邮路问题。

In graph theory, a branch of mathematics and computer science, the Chinese postman problem (CPP), postman tour or route inspection problem is to find a shortest closed path or circuit that visits every edge of a (connected) undirected graph. When the graph has an Eulerian circuit (a closed walk that covers every edge once), that circuit is an optimal solution. Otherwise, the optimization problem is to find the smallest number of graph edges to duplicate (or the subset of edges with the minimum possible total weight) so that the resulting multigraph does have an Eulerian circuit. It may be solved in polynomial time.