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: König's theorem in graph theory | Statement: [Julius König, knownFor, König's theorem in graph theory]

Target entity: König's theorem in graph theory
Context triple: [Julius König, knownFor, König's theorem in graph theory]

• A. 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.
• 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. Kuratowski’s theorem on planar graphs
  Kuratowski’s theorem on planar graphs is a fundamental result in graph theory that characterizes planar graphs by stating that a finite graph is planar if and only if it contains no subgraph that is a subdivision of the complete graph K₅ or the complete bipartite graph K₃,₃.
• 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. 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.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: König's theorem in graph theory
Target entity description: 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.

• A. 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.
• 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. Kuratowski’s theorem on planar graphs
  Kuratowski’s theorem on planar graphs is a fundamental result in graph theory that characterizes planar graphs by stating that a finite graph is planar if and only if it contains no subgraph that is a subdivision of the complete graph K₅ or the complete bipartite graph K₃,₃.
• 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. 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.
• F. None of above. chosen