Dirac–Motzkin conjecture

Target entity: Dirac–Motzkin conjecture
Context triple: [Sylvester–Gallai theorem, relatedTo, Dirac–Motzkin conjecture]

• A. Sylvester–Gallai theorem
  The Sylvester–Gallai theorem is a result in incidence geometry stating that for any finite set of points in the Euclidean plane not all on a single line, there exists a line that passes through exactly two of the points.
• B. Szemerédi–Trotter theorem
  The Szemerédi–Trotter theorem is a fundamental result in combinatorial geometry that gives near-optimal upper bounds on the number of incidences between points and lines in the plane.
• C. de Bruijn–Erdős theorem
  The de Bruijn–Erdős theorem is a fundamental result in combinatorics and graph theory that relates finite and infinite structures, notably asserting that certain properties of infinite graphs or set systems are determined by their finite substructures.
• D. Conway's thrackle conjecture
  Conway's thrackle conjecture is an unsolved problem in combinatorial geometry asserting that in any drawing of a graph where every pair of edges meets exactly once, the number of edges cannot exceed the number of vertices.
• E. Erdős–Szekeres theorem
  The Erdős–Szekeres theorem is a fundamental result in combinatorial geometry that guarantees the existence of large convex polygons within sufficiently large sets of points in the plane in general position.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Dirac–Motzkin conjecture
Target entity description: The Dirac–Motzkin conjecture is a statement in combinatorial geometry about the minimum number of ordinary lines (lines containing exactly two points) determined by a finite set of points in the plane.

• A. Sylvester–Gallai theorem
  The Sylvester–Gallai theorem is a result in incidence geometry stating that for any finite set of points in the Euclidean plane not all on a single line, there exists a line that passes through exactly two of the points.
• B. Szemerédi–Trotter theorem
  The Szemerédi–Trotter theorem is a fundamental result in combinatorial geometry that gives near-optimal upper bounds on the number of incidences between points and lines in the plane.
• C. de Bruijn–Erdős theorem
  The de Bruijn–Erdős theorem is a fundamental result in combinatorics and graph theory that relates finite and infinite structures, notably asserting that certain properties of infinite graphs or set systems are determined by their finite substructures.
• D. Conway's thrackle conjecture
  Conway's thrackle conjecture is an unsolved problem in combinatorial geometry asserting that in any drawing of a graph where every pair of edges meets exactly once, the number of edges cannot exceed the number of vertices.
• E. Erdős–Szekeres theorem
  The Erdős–Szekeres theorem is a fundamental result in combinatorial geometry that guarantees the existence of large convex polygons within sufficiently large sets of points in the plane in general position.
• F. None of above. chosen