Is it possible for a citizen of Königsberg to make a tour of the city and cross each bridge exactly twice? (See Figure 10.1.1.) Explain.
Is it possible for a citizen of Konigsberg to make a tour of the city and cross every bridge exactly twice? Why?
An Euler circuit is a circuit that contains every edge of the graph.
A connected graph has an Euler circuit if and only if each of the vertices has an even degree.
Let us first create a graph that corresponds with the given figure. Each region is represented by a vertex and each bridge between two regions is represented by an edge between two corresponding vertices.
We then obtain the following graph.
We need to cross each bridge exactly twice...
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