2.1.2 - Dirac's Theorem
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Practice Questions
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What is a Hamiltonian circuit?
💡 Hint: Think about paths that start and end at the same point.
State Dirac's Theorem.
💡 Hint: Focus on vertex degrees in relation to the number of vertices.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does Dirac's Theorem state?
💡 Hint: Focus on the degree condition related to connected graphs.
True or False: Ore's condition is more restrictive than Dirac's.
💡 Hint: Consider the flexibility in vertex degree comparisons.
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Challenge Problems
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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.
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.
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