In Chapter 1 we met two puzzles that could be modeled by graphs: the Königsberg bridge problem and Hamilton’s game. There are many other games and puzzles which can be profitably analysed by using graph theoretic concepts, as will be seen in Section 11.5. This is because many puzzles and games can be converted into an equivalent graph theoretic problem in which the solution can be found by attempting to construct either an Eulerian trail or a Hamiltonian cycle within an appropriate graph. We begin with Eulerian graphs.
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