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Bondy and Chvátal theorem (Theorem)

Bondy and Chvátal's theorem.
Let $ G$ be a graph of order $ n\ge 3$ and suppose that $ u$ and $ v$ are distinct non adjacent vertices such that $ \deg(u)+\deg(v)\ge n$.

Then $ G$ is Hamiltonian if and only if $ G+uv$ is Hamiltonian.



"Bondy and Chvátal theorem" is owned by drini. [ full author list (3) | owner history (1) ]
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See Also: Hamiltonian graph, Ore's theorem


Attachments:
proof of Bondy and Chvátal theorem (Proof) by taxipom
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Cross-references: Hamiltonian, adjacent vertices, order, graph
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This is version 4 of Bondy and Chvátal theorem, born on 2001-10-24, modified 2006-10-23.
Object id is 479, canonical name is BondyAndChvatalTheorem.
Accessed 3742 times total.

Classification:
AMS MSC: 05C45 (Combinatorics :: Graph theory :: Eulerian and Hamiltonian graphs)
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