Practice Ore's Condition - 2.1.3 | 2. Hamiltonian Circuit | Discrete Mathematics - Vol 3
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Ore's Condition

2.1.3 - Ore's Condition

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define a Hamiltonian circuit.

💡 Hint: Think about the criteria for visiting vertices in a closed loop.

Question 2 Easy

What is Ore's condition in relation to Hamiltonian graphs?

💡 Hint: Consider the role of vertex degrees in forming connections.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is a Hamiltonian circuit?

A circuit that visits each vertex once
A circuit that visits some vertices
A circuit that can revisit vertices

💡 Hint: A Hamiltonian tour avoids repetition.

Question 2

True or False: Ore's condition must always guarantee a Hamiltonian cycle.

True
False

💡 Hint: Consider graphs that satisfy Ore's condition without forming cycles.

2 more questions available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Analyze a graph with vertices A, B, C, D, E arranged such that A-B, A-C, C-D, D-E are edges. Determine if Ore's condition holds and justify your conclusion.

💡 Hint: Be methodical in your degree counts and remember the basics of degree sums.

Challenge 2 Hard

Design a minimal graph of 7 characters where Ore's condition is satisfied, but the graph is not Hamiltonian. Explain your configuration.

💡 Hint: Focus on distributing vertex connections strategically.

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