1. Euler Path and Euler Circuit

Try these first

1. 1.

   What is an Euler circuit?

   Hint

   Consider how the path starts and ends.

2. 2.

   How many vertices must have odd degrees for an Euler path?

   Hint

   Reflect on how many endpoints an Euler path has.

3. 3.

   What defines an Euler circuit?

   • It must start and end at the same vertex
   • It must have odd degree vertices
   • It must only use cut edges

   Hint

   Think about the path's start and endpoints.

4. 4.

   True or False: An Euler path can exist in a graph with all vertices having even degrees.

   • True
   • False

   Hint

   Reflect on Euler path conditions.

5. 5.

   Design a graph with 4 vertices of which 2 have odd degrees and 2 have even degrees. Show if it has an Euler path and explain your reasoning.

   Hint

   Check how many vertices have even and odd degrees.

6. 6.

   Using Fleury's algorithm, find the Euler circuit for a given graph diagram (provided in class). Describe each step.

   Hint

   Focus on the edges remaining as you traverse.