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2 cards from this section. Quick, good the night before a test.
Define a Hamiltonian circuit.
Think of a tour that starts and ends at the same vertex.
What does Dirac's theorem specify regarding vertex degrees?
Recall the minimum degree condition.
What is a Hamiltonian circuit?
Think about what must be visited in a circuit.
True or False: Dirac's Theorem is both necessary and sufficient for a graph to be Hamiltonian.
Consider examples that defy this condition.
Design a graph with 6 vertices that adheres to Ore's condition and prove it is Hamiltonian.
Start with vertices connected linearly, then add links that do not disrupt the required sums.
Prove or disprove Ore's theorem on a bipartite graph by illustrating vertex pairs.
Consider how bipartite graphs are structured and whether all vertex combinations meet Ore's condition.
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