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: Hoffman bound in graph theory | Statement: [Alan Hoffman, notableConcept, Hoffman bound in graph theory]

Target entity: Hoffman bound in graph theory
Context triple: [Alan Hoffman, notableConcept, Hoffman bound in graph theory]

• A. Alon–Boppana bound
  The Alon–Boppana bound is a fundamental result in spectral graph theory that gives an asymptotic lower bound on the second-largest eigenvalue of large regular graphs, showing inherent limitations on how well such graphs can approximate expanders.
• B. 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.
• 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. 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.
• E. 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.
• 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: Hoffman bound in graph theory
Triple: [Alan Hoffman, notableConcept, Hoffman bound in graph theory]

The Hoffman bound in graph theory is a spectral bound that uses the eigenvalues of a graph’s adjacency matrix to give an upper limit on the size of its maximum independent set (and related parameters like the chromatic number).

Target entity: Hoffman bound in graph theory
Target entity description: The Hoffman bound in graph theory is a spectral bound that uses the eigenvalues of a graph’s adjacency matrix to give an upper limit on the size of its maximum independent set (and related parameters like the chromatic number).

• A. Alon–Boppana bound
  The Alon–Boppana bound is a fundamental result in spectral graph theory that gives an asymptotic lower bound on the second-largest eigenvalue of large regular graphs, showing inherent limitations on how well such graphs can approximate expanders.
• B. 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.
• 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. 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.
• E. 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.
• F. None of above. chosen