Euler 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

Circuits start and stop at

• same vertex

• different vertices

This graph will have an Euler Circuit.

• True

• False

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

Which of the graphs below have Euler circuits?

• I only

• II only

• Both I and II

• Neither I and II

Which of the graphs below have Euler circuits?

• I only

• II only

• Both I and II

• Neither I and II

Which of the graphs below have Euler circuits?

• I only

• II only

• Both I and II

• Neither I or II

What is the valence (degree) of vertex A in the graph ?

• 3

• 5

• 7

• 11

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.

This graph will have an Euler Path.

• True

• False