Bondy–Chvátal theorem

E1336827 UNEXPLORED

The Bondy–Chvátal theorem is a fundamental result in graph theory that characterizes when a graph can be extended to a Hamiltonian graph via closure operations, providing a powerful tool for proving the existence of Hamiltonian cycles.

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All labels observed (3)

Label	Occurrences
Chvátal–Erdős theorem	2
Bondy–Chvátal theorem canonical	1
Chvátal’s theorem	1

How this entity was disambiguated

This entity first appeared as the object of triple T18628480 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Bondy–Chvátal theorem
Context triple: [Hamiltonian cycle, sufficientCondition, Bondy–Chvátal theorem]

A. Ore's theorem
Ore's theorem is a fundamental result in graph theory that gives a degree-based criterion guaranteeing a simple graph contains a Hamiltonian cycle.
B. Gallai theorem
Gallai's theorem is a fundamental result in graph theory and Ramsey theory that characterizes the structure of colorings of complete graphs by guaranteeing large monochromatic or well-organized subgraphs.
C. Turán's theorem
Turán's theorem is a fundamental result in extremal graph theory that determines the maximum number of edges a graph can have without containing a complete subgraph of a given size.
D. Dirac's theorem
Dirac's theorem is a fundamental result in graph theory that gives a simple degree condition on the vertices of a finite graph guaranteeing the existence of a Hamiltonian cycle.
E. Erdős–Gallai theorem
The Erdős–Gallai theorem is a fundamental result in graph theory that characterizes which sequences of nonnegative integers can occur as the degree sequences of simple graphs.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Bondy–Chvátal theorem
Target entity description: The Bondy–Chvátal theorem is a fundamental result in graph theory that characterizes when a graph can be extended to a Hamiltonian graph via closure operations, providing a powerful tool for proving the existence of Hamiltonian cycles.

A. Ore's theorem
Ore's theorem is a fundamental result in graph theory that gives a degree-based criterion guaranteeing a simple graph contains a Hamiltonian cycle.
B. Gallai theorem
Gallai's theorem is a fundamental result in graph theory and Ramsey theory that characterizes the structure of colorings of complete graphs by guaranteeing large monochromatic or well-organized subgraphs.
C. Turán's theorem
Turán's theorem is a fundamental result in extremal graph theory that determines the maximum number of edges a graph can have without containing a complete subgraph of a given size.
D. Dirac's theorem
Dirac's theorem is a fundamental result in graph theory that gives a simple degree condition on the vertices of a finite graph guaranteeing the existence of a Hamiltonian cycle.
E. Erdős–Gallai theorem
The Erdős–Gallai theorem is a fundamental result in graph theory that characterizes which sequences of nonnegative integers can occur as the degree sequences of simple graphs.
F. None of above. chosen