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