Euler’s Formula

Abstract

In Chapter 11 we considered problems that can be cast in the language of graph theory: If we draw some special graphs in the plane, into how many parts do these graphs divide the plane? Indeed, we start with a set of lines; we consider the intersections of the given lines as nodes of the graph, and the segments arising on these lines as the edges of our graph. (For the time being, let us forget about the infinite half-lines. We’ll come back to the connection between graphs and sets of lines later.)