Euler and Hamilton (Paths and Cricuits)

Which of the following is a Hamilton circuit of the graph?

• ABCDEFGA
• ACBEGFDA
• CBGEDFAC
• CEGBADFC

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

• True

• False

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

Circuits start and stop at 

• same vertex
• different vertices

Paths start and stop at

• same vertex
• different vertices

Euler paths 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.

• A graph with one odd vertex will have an Euler Path but not an Euler Circuit.

Does this graph have an Euler Path, Euler Circuit, both, or neither?

• Euler Path

• Euler Circuit

• Both

• Neither

Hamilton touches

• all edges
• all vertices

This graph will have a Euler's Path. 

• True
• False