Chapter 6 Test: Euler and Hamilton Circuits and Paths

Tracing all edges on a figure without picking up your pencil and repeating and starting and stopping in the same spot

• Euler Circuit

• Euler Path

True or false: With Hamilton circuits, every edge must be used. With Euler circuits, every vertex must be used.

• True
• False

Circuits start and stop at 

• same vertex
• different vertices

Paths start and stop at

• same vertex
• different vertices

Euler circuits must touch

• all edges

• all vertices

Which of the following is false?

• Euler Paths exist when there are exactly two vertices of odd degree.
• Euler circuits exist when the degree of all vertices are even.
• A graph with more than two odd vertices will never have an Euler Path or Circuit.
• A graph with one odd vertex will have an Euler Path but not an Euler Circuit.

Touching all vertices in a figure without repeating or picking up your pencil and starting and stopping at different spots

• Euler Circuit
• Euler Path
• Hamilton Circuit
• Hamilton Path

Touching all vertices in a figure without repeating or picking up your pencil and starting and stopping at same spot

• Euler Circuit
• Euler Path
• Hamilton Circuit
• Hamilton Path

Hamilton touches

• all edges
• all vertices

Tracing all edges on a figure without picking up your pencil or repeating and starting and stopping at different spots

• Euler Circuit
• Euler Path