Homework Hints 9-1

[tippy title=”Problems 1-5″]Problems 1-5
There questions are basically definitions and procedures. Read the book and then paraphrase each in your own words.[/tippy]

[tippy title=”Problems 6-11″]Problems 6-11
Classify each vertex as even or odd to use Euler’s circuit theorem. If an Euler circuit exists, then start at one of the even vertices to draw the circuit. See Example 3.[/tippy]

[tippy title=”Problems 12-17″]Problems 12-17
You can either use trial-and-error or the nearest-neighbor method to find a Hamiltonian cycle. See Example 5.[/tippy]

[tippy title=”Problems 18-23″]Problems 18-23
Classify each room as even or odd according to the number of doors in each room, and then use Euler’s circuit theorem. If it is an Euler circuit, then begin in an even room to draw the circuit. See Example 4.[/tippy]

[tippy title=”Problems 24-27″]Problems 24-27
Classify each vertex as even or odd and use Euler’s circuit theorem. If there is an Euler circuit, then start an an even vertex and draw the circuit. See Example 3.[/tippy]

[tippy title=”Problems 28-31″]Problems 28-31
Either use trial-and-error or the Nearest Neighbor method to find a Hamiltonian cycle. See Example 6.[/tippy]

[tippy title=”Problem 32″]Problem 32
See Example 2 and Table 9.1, and then apply Euler’s circuit theorem.[/tippy]

[tippy title=”Problem 33″]Problem 33
See Example 5. One possible solution:
1, 6, 7, 8, 9, 10, 11, 12, 13, 19, 18, 17, 16, 20, 15, 14, 5, 4, 3, 2, 1.
Can you find another?[/tippy]

[tippy title=”Problems 34-40″]Problems 34-40
See Example 2 and Table 9.1, and then apply Euler’s circuit theorem.[/tippy]