1.3. References

Try these first

1. 1.

   Define Euler Circuit.

   Hint

   Think about circuits and where they start and end.

2. 2.

   What is needed for an Euler Path to exist?

   Hint

   Consider what happens when a vertex has an odd number of edges.

3. 3.

   What defines an Euler Circuit?

   • Visits every edge once and ends at a different vertex
   • Visits every edge once and returns to the starting vertex
   • Only visits some edges

   Hint

   Think about the shape it makes.

4. 4.

   Can a graph with all vertices of odd degree have an Euler Circuit?

   • True
   • False

   Hint

   Recall the conditions for Euler paths and circuits.

5. 5.

   Given a connected multigraph with vertices of degrees 4, 4, 2, and 2, is it possible to form an Euler Circuit? Justify your answer.

   Hint

   Verify the degrees of all vertices.

6. 6.

   Create a graph with five vertices where two have odd degrees and demonstrate an Euler path using Fleury's algorithm.

   Hint

   Think about how edges connect these vertices.