The city of Honigsberg, located on the banks of the Rregel River, had eight brid

Question

The city of Honigsberg, located on the banks of the Rregel River, had eight bridges that connected islands in the river to the shores as illustrated below. It was the custom of the town people to stroll on Friday afternoons and, in particular, to cross over the bridges. The people of Honigsberg wanted to know if it was possible to stroll in such a way that it was possible to go over each bridge exactly once and return to the starting point. a.) Is the problem looking for an Euler circuit or a Hamiltonian circuit? b.) Draw a graph with nodes and edges to show the situation. c.) If there is a way, show the detailed circuit; otherwise, use an appropriate theorem to justify your answer. Link to illustration: http://i53.tinypic.com/avor38.jpg

Explanation / Answer

Problem looking for Hamiltonian circuit as it is a undirected graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a cycle in an undirected graph which visits each vertex exactly once and also returns to the starting verte x. e.

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