A 2 by 2 grid graph. The graph shown in Fig. 51 represents a street grid that is 2

Chapter 6, Problem 63

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A 2 by 2 grid graph. The graph shown in Fig. 51 represents a street grid that is 2 blocks by 2 blocks. (Such a graph is called a 2 by 2 grid graph.) For convenience, the vertices are labeled by type: corner vertices C1, C2, C3, and C4, boundary vertices B1, B2, B3, and B4, and the interior vertex I. (a) Find a Hamilton path in the graph that starts at I. (b) Find a Hamilton path in the graph that starts at one of the corner vertices and ends at a different corner vertex. (c) Find a Hamilton path that starts at one of the corner vertices and ends at I. (d) Find (if you can) a Hamilton path that starts at one of the corner vertices and ends at one of the boundary vertices. If this is impossible, explain why. B1 B3 C1 C2 C4 C3 B4 I B2 FIgurE 51

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