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: Hamiltonian path problem | Statement: [Seven Bridges of Königsberg problem, relatedTo, Hamiltonian path problem]

Target entity: Hamiltonian path problem
Context triple: [Seven Bridges of Königsberg problem, relatedTo, Hamiltonian path problem]

• A. Hamiltonian cycle concept chosen
  The Hamiltonian cycle concept is a fundamental idea in graph theory describing a cycle that visits each vertex of a graph exactly once and returns to the starting point.
• B. Seven Bridges of Königsberg problem
  The Seven Bridges of Königsberg problem is a historic puzzle in graph theory that asks whether one can walk through the city of Königsberg crossing each of its seven bridges exactly once, leading Euler to found the field of topology.
• C. Happy Ending problem
  The Happy Ending problem is a famous combinatorial geometry question that investigates the minimum number of points in general position in the plane needed to guarantee the existence of a convex polygon with a given number of vertices.
• D. A Combinatorial Problem
  "A Combinatorial Problem" is a classic mathematical paper by N. G. de Bruijn that introduces and analyzes a fundamental counting problem in combinatorics.
• E. Conway's 99-graph problem
  Conway's 99-graph problem is an unsolved combinatorial question in graph theory, posed by John H. Conway, concerning the existence and properties of a hypothetical 99-vertex graph with highly constrained adjacency conditions.
• F. None of above.
• G. Unsure - the case is ambiguous/there is not enough information to decide.