Constructing of OE-postman path for a planar graph

With automated preparation of the cutting process, the cutting plan can be represented as a flat graph. The purpose of this simulation is to determine the shortest path of the cutting tool, provided that the part cut from the sheet would not require additional cuts. The article deals with the task of building the path of the Chinese postman in a flat graph, which is a model of the cutting plan. An orderly coverage condition is imposed on this path (i.e., the cycle of traversed edges does not encompass those not yet traversed). Such a path will also be called an OE path. This limitation means the absence of additional cuts for parts. The article discusses the recursive algorithm for constructing such chains. It is proved that the algorithm has polynomial complexity. The developed software allows solving the problem for an arbitrary flat graph. The program has been tested for various types of flat graphs.