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

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

• A. Bondy–Chvátal theorem chosen
  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.
• B. 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.
• C. 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.
• D. 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.
• E. Erdős–Stone theorem
  The Erdős–Stone theorem is a fundamental result in extremal graph theory that asymptotically determines the maximum number of edges in an n-vertex graph that avoids containing a given subgraph.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.