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: Dirac's theorem | Statement: [Hamiltonian cycle, sufficientCondition, Dirac's theorem]

Target entity: Dirac's theorem
Context triple: [Hamiltonian cycle, sufficientCondition, Dirac's theorem]

• A. 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.
• B. 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.
• 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. König's theorem in graph theory
  König's theorem in graph theory is a fundamental result in bipartite graphs stating that the size of a maximum matching equals the size of a minimum vertex cover.
• E. Menger theorem in graph theory
  Menger's theorem in graph theory is a fundamental result that characterizes the connectivity between two vertices in a graph by equating the maximum number of pairwise internally disjoint paths between them with the minimum size of a vertex cut separating them.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Dirac's theorem
Target entity description: 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.

• A. 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.
• B. 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.
• 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. König's theorem in graph theory
  König's theorem in graph theory is a fundamental result in bipartite graphs stating that the size of a maximum matching equals the size of a minimum vertex cover.
• E. Menger theorem in graph theory
  Menger's theorem in graph theory is a fundamental result that characterizes the connectivity between two vertices in a graph by equating the maximum number of pairwise internally disjoint paths between them with the minimum size of a vertex cut separating them.
• F. None of above. chosen

Target predicate: sufficientCondition
Context triple: [Hamiltonian cycle, sufficientCondition, Dirac's theorem]

• A. sufficientConditionFor chosen
  Indicates that the truth or occurrence of one entity guarantees or ensures the truth or occurrence of another entity.
• B. supportsCondition
  Indicates that one entity helps maintain, enable, or is compatible with a particular condition or state in another entity.
• C. holdsUnderCondition
  Indicates that one fact, rule, or relationship remains valid only when a specified condition or set of conditions is satisfied.
• D. obligationCondition
  Indicates that one situation or state serves as the condition under which an obligation for an entity becomes active or must be fulfilled.
• E. presentCondition
  Indicates that an entity currently has or exhibits a particular state, situation, or condition.
• F. None of above.