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Traversable (Euler-Trail) Graphs

Master Euler trails in graphs with interactive lessons and practice problems! Designed for students like you!

Understanding Euler Trails in Graphs

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Video explanation of this concept

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Beginner

Start here! Easy to understand

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Beginner Explanation

An Euler trail is a path that uses every edge exactly once. For a connected graph, it exists if exactly 0 or 2 vertices have odd degree. If 0, it is a circuit; if 2, the trail starts and ends at the odd vertices.

Practice Problems

Test your understanding with practice problems

1

Quick Quiz

Single Choice Quiz
Beginner

In a connected graph with vertex degrees 2, 3, 3, 4, does it have an Euler trail?

Please select an answer for all 1 questions before checking your answers. 1 question remaining.
2

Real-World Problem

Question Exercise
Intermediate

Teenager Scenario

Four towns A, B, C, D are connected by roads forming a connected graph. The degrees are deg(A)=3, deg(B)=2, deg(C)=1, deg(D)=2. Determine if an Euler trail exists.
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3

Thinking Challenge

Thinking Exercise
Intermediate

Think About This

Can a connected graph with degrees 1, 3, 3, 2, 4 have an Euler trail?

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4

Challenge Quiz

Single Choice Quiz
Advanced

A connected graph has vertices with degrees 3, 3, 3, 3, 2, 2. Is there an Euler trail?

Please select an answer for all 1 questions before checking your answers. 1 question remaining.

Recap

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Review key concepts and takeaways