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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a Hamiltonian circuit?
💡 Hint: Think about paths that start and end at the same point.
Question 2
Easy
State Dirac's Theorem.
💡 Hint: Focus on vertex degrees in relation to the number of vertices.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What does Dirac's Theorem state?
- The sum of the degrees of non-adjacent vertices is always less than n.
- A connected graph is Hamiltonian if every vertex has degree at least n/2.
- All Eulerian graphs are Hamiltonian.
💡 Hint: Focus on the degree condition related to connected graphs.
Question 2
True or False: Ore's condition is more restrictive than Dirac's.
- True
- False
💡 Hint: Consider the flexibility in vertex degree comparisons.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a connected graph of 8 vertices where each vertex has a degree of 4, is the graph Hamiltonian? Explain with reference to Dirac's Theorem.
💡 Hint: Check if the vertex degrees meet the necessary condition.
Question 2
Construct a graph with 6 vertices that satisfies Ore's condition yet lacks a Hamiltonian circuit. Demonstrate how.
💡 Hint: Consider what non-adjacency and degree sums indicate toward connectivity.
Challenge and get performance evaluation