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: Ahlswede–Khachatrian complete intersection theorem | Statement: [Erdős–Ko–Rado theorem, hasGeneralization, Ahlswede–Khachatrian complete intersection theorem]

Target entity: Ahlswede–Khachatrian complete intersection theorem
Context triple: [Erdős–Ko–Rado theorem, hasGeneralization, Ahlswede–Khachatrian complete intersection theorem]

• A. Erdős–Ko–Rado theorem
  The Erdős–Ko–Rado theorem is a fundamental result in extremal combinatorics that determines the maximum size of a family of subsets of a finite set in which every pair of subsets has a non-empty intersection.
• B. Graham–Pollak theorem
  The Graham–Pollak theorem is a result in graph theory that states the edges of a complete graph on n vertices cannot be partitioned into fewer than n−1 complete bipartite subgraphs.
• C. Combinatorial Nullstellensatz
  Combinatorial Nullstellensatz is a powerful algebraic tool in combinatorics that uses polynomial methods over fields to derive results about combinatorial structures, such as existence and counting theorems.
• D. Pósa’s theorem in graph theory
  Pósa’s theorem in graph theory is a result that gives a sufficient degree condition for a finite graph to contain a Hamiltonian cycle.
• E. Szemerédi's theorem
  Szemerédi's theorem is a fundamental result in combinatorial number theory stating that any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Ahlswede–Khachatrian complete intersection theorem
Target entity description: The Ahlswede–Khachatrian complete intersection theorem is a fundamental result in extremal set theory that fully characterizes the largest intersecting families of k-element subsets for all parameter ranges, extending and sharpening the Erdős–Ko–Rado theorem.

• A. Erdős–Ko–Rado theorem
  The Erdős–Ko–Rado theorem is a fundamental result in extremal combinatorics that determines the maximum size of a family of subsets of a finite set in which every pair of subsets has a non-empty intersection.
• B. Graham–Pollak theorem
  The Graham–Pollak theorem is a result in graph theory that states the edges of a complete graph on n vertices cannot be partitioned into fewer than n−1 complete bipartite subgraphs.
• C. Combinatorial Nullstellensatz
  Combinatorial Nullstellensatz is a powerful algebraic tool in combinatorics that uses polynomial methods over fields to derive results about combinatorial structures, such as existence and counting theorems.
• D. Pósa’s theorem in graph theory
  Pósa’s theorem in graph theory is a result that gives a sufficient degree condition for a finite graph to contain a Hamiltonian cycle.
• E. Szemerédi's theorem
  Szemerédi's theorem is a fundamental result in combinatorial number theory stating that any subset of the integers with positive upper density contains arbitrarily long arithmetic progressions.
• F. None of above. chosen