Triple

T18628480
Position Surface form Disambiguated ID Type / Status
Subject Hamiltonian cycle E455347 entity
Predicate sufficientCondition P94877 FINISHED
Object Bondy–Chvátal theorem — NE NERFINISHED

How this triple was built (3 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
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).
Input
Phrase: Bondy–Chvátal theorem | Statement: [Hamiltonian cycle, sufficientCondition, Bondy–Chvátal theorem]
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

Provenance (2 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69d8d38cc7948190a55ea64e5638994e completed April 10, 2026, 10:40 a.m.
NER Named-entity recognition batch_69e54f063a1c819087e544c64f5cf80f completed April 19, 2026, 9:54 p.m.
Created at: April 10, 2026, 11:46 a.m.