Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Bondy–Chvátal theorem | Statement: [Hamiltonian cycle, sufficientCondition, Bondy–Chvátal theorem]

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.

Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"

Entity: Bondy–Chvátal theorem
Triple: [Hamiltonian cycle, sufficientCondition, Bondy–Chvátal theorem]

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.

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