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: Hopcroft–Tarjan planarity algorithm | Statement: [John E. Hopcroft, knownFor, Hopcroft–Tarjan planarity algorithm]

Target entity: Hopcroft–Tarjan planarity algorithm
Context triple: [John E. Hopcroft, knownFor, Hopcroft–Tarjan planarity algorithm]

• A. Lipton–Tarjan separator theorem
  The Lipton–Tarjan separator theorem is a fundamental result in graph theory that shows any planar graph can be efficiently divided into roughly equal parts by removing only a relatively small set of vertices, enabling faster algorithms for many computational problems.
• B. 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.
• C. Tarjan's strongly connected components algorithm
  Tarjan's strongly connected components algorithm is a classic linear-time graph algorithm that efficiently identifies all strongly connected components in a directed graph using depth-first search and low-link values.
• D. Fleury's algorithm
  Fleury's algorithm is a classical graph-theoretic procedure for systematically finding an Eulerian trail by repeatedly choosing edges that are not bridges unless necessary.
• E. Hierholzer's algorithm
  Hierholzer's algorithm is a classical graph algorithm that efficiently constructs an Eulerian trail or circuit by iteratively building and merging cycles in a graph where such a trail exists.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Hopcroft–Tarjan planarity algorithm
Target entity description: The Hopcroft–Tarjan planarity algorithm is a classic linear-time graph algorithm that determines whether a graph can be drawn in the plane without edge crossings and, if so, constructs such an embedding.

• A. Lipton–Tarjan separator theorem
  The Lipton–Tarjan separator theorem is a fundamental result in graph theory that shows any planar graph can be efficiently divided into roughly equal parts by removing only a relatively small set of vertices, enabling faster algorithms for many computational problems.
• B. 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.
• C. Tarjan's strongly connected components algorithm
  Tarjan's strongly connected components algorithm is a classic linear-time graph algorithm that efficiently identifies all strongly connected components in a directed graph using depth-first search and low-link values.
• D. Fleury's algorithm
  Fleury's algorithm is a classical graph-theoretic procedure for systematically finding an Eulerian trail by repeatedly choosing edges that are not bridges unless necessary.
• E. Hierholzer's algorithm
  Hierholzer's algorithm is a classical graph algorithm that efficiently constructs an Eulerian trail or circuit by iteratively building and merging cycles in a graph where such a trail exists.
• F. None of above. chosen