1.3 Beyond Euler Circuits- Video

Key Ideas If a graph has an odd number of vertices, then any circuit must reuse at least one edge. The Chinese postman problem involves finding a circuit that reuses as few edges as possible. Reusing an edge that joins two vertices is like adding a new edge between those vertices. Adding new edges that duplicate existing edges to a connected graph and produce an Euler circuit of a graph is called eulerizing the original graph. An Euler circuit on an eulerized graph can be “squeezed” into a circuit on the original graph by reusing precisely those edges that correspond to the edges added in the eulerization.