Graph Theory

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

• Euler Circuit
• Euler Path

Euler paths must touch

• all edges
• all vertices

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

• Euler Path
• Euler Circuit
• Both
• Neither

This graph will have a Euler's Path. 

• True
• False

Does this graph have a Euler's Path? 

• True
• False

Is the following graph complete?

• Yes

• No

In the graph above, which of the following statements is true?

• A is adjacent to E

• A is not adjacent to D

• C is adjacent to D

• C is not adjacent to E

Tags

CCSS.4.G.A.1

Using the following tournament information, construct a directed graph and find a ranking of the participants:

Between A and B, A wins

Between A and C, C wins

Between A and D, D wins

Between B and C, C wins

Between B and D, D wins

Between C and D, C wins

• 1st place: A, 2nd place: B, 3rd place: C, 4th place: D

• 1st place: B, 2nd place: A, 3rd place: D, 4th place: C

• 1st place: C, 2nd place: D, 3rd place: A, 4th place: B

• 1st place: D, 2nd place: C, 3rd place: B, 4th place: A

In how many colors can you color this picture, following the rules of the 4 color theorem?

• 1

• 2

• 3

• 4

What is the chromatic number of the graph?

• 1

• 2

• 3

• 4