Euler and Hamiltonian Paths and Circuits

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

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

• True
• False

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

• Euler Path
• Euler Circuit
• Neither

How do we quickly determine if a graph will have a Euler's Circuit? 

• All even degree verticies
• Exactly 2 odd degree verticies
• Every Vertex will be used once
• I have no clue

How do we quickly determine if the graph will have a Euler's Path

• All even degree verticies
• Exactly 2 odd degree verticies
• Each vertex will be used once
• I have no clue. 

A given graph has vertices with the given degrees:  3, 5, 6, 8, 2
What is DEFINITELY TRUE? 

• This graph will be a Euler's Curcuit
• This graph will be a Euler's Path
• This graph will be a Hamiltonian Path
• I need more information

A graph has the vertices with the following degrees: 4, 6, 8, 2, 2, 6, 4
What do we DEFINITELY KNOW?

• This will have a Euler's Circuit
• This will have a Euler's Path
• This will have a Hamiltonian Path
• We need more information

This graph will have a Euler's Circuit

• True
• False