Euler and Hamilton Paths and Circuits

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

• ABCDEFGA
• ACBEGFDA
• CBGEDFAC
• CEGBADFC

List a path from vertex D to vertex G

• DAFCEBG
• DFACEBG
• DECAFBG
• DCBAFEG

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

• 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

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

• Euler Circuit
• Euler Path

Circuits start and stop at 

• same vertex
• different vertices

Paths start and stop at

• same vertex
• different vertices

Tags

CCSS.HSA.REI.D.11

CCSS.HSG.CO.A.1

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 or Circuit.
• 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