Chapter 6, Problem 66E

66. m by n grid graphs. An m by n grid graph represents a rectangular street grid that is m. blocks by n blocks, as indicated in $\underset{\_}{Fig.6-51.}$

$Figure6-51$

a. If m and n are both odd, then the m by n grid graph has a Hamilton circuit. Describe the circuit by drawing it on a generic graph.

b. If either m or n is even and the other one is odd, then the m by n grid graph has Hamilton circuit. Describe the circuit by drawing it on a generic graph.

c. . If m and n are both even, then the m by n grid graph does not have a Hamilton circuit. Explain why a Hamilton circuit is impossible.