02/10/09
Math 232: Quiz 4
Name:
Instructions
•Show all your work in the space provided. No credit will be given to correct answers
with no supporting work.
•If provided, write your final answer in the box.
1. [5] How many Hamilton cycles are there in the graph K3,3?
Solution: Consider the graph K3,3below
abc
def
Choosing alternating vertices from the two partition sets, we have 6×3×2×2×1×1 = 72
possible cycles where one point is fixed and the cycle has a direction. Since Hamilton
cycles use all vertices, we divide by 6 to remove the dependency of the starting vertex.
To get the total amount of undirected cycles, we also must divide by 2. Hence the total
number of Hamilton cycles is 72/12 = 6.
