Practice References - 1.3 | 1. Euler Path and Euler Circuit | Discrete Mathematics - Vol 3
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1.3 - References

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define Euler Circuit.

💡 Hint: Think about circuits and where they start and end.

Question 2 Easy

What is needed for an Euler Path to exist?

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

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

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.

Question 2

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

True
False

💡 Hint: Recall the conditions for Euler paths and circuits.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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.

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Reference links

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