Alon–Tarsi conjecture

Target entity: Alon–Tarsi conjecture
Context triple: [Noga Alon, notableWork, Alon–Tarsi conjecture]

• A. Erdős–Ko–Rado theorem
  The Erdős–Ko–Rado theorem is a fundamental result in extremal combinatorics that determines the maximum size of a family of subsets of a finite set in which every pair of subsets has a non-empty intersection.
• B. 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.
• C. Sylvester’s theorem on partitions
  Sylvester’s theorem on partitions is a result in number theory that provides a systematic way to count integer partitions subject to certain congruence or restriction conditions, forming part of the foundational work in partition theory.
• D. Sylvester determinant
  The Sylvester determinant is a mathematical construct introduced by James Joseph Sylvester, typically referring to a determinant associated with resultants and elimination theory in algebra.
• E. Szekeres–Lindström theorem
  The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Alon–Tarsi conjecture
Target entity description: The Alon–Tarsi conjecture is a prominent open problem in combinatorics and graph theory concerning orientations and colorings of graphs, with deep connections to Latin squares and polynomial method techniques.

• A. Erdős–Ko–Rado theorem
  The Erdős–Ko–Rado theorem is a fundamental result in extremal combinatorics that determines the maximum size of a family of subsets of a finite set in which every pair of subsets has a non-empty intersection.
• B. 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.
• C. Sylvester’s theorem on partitions
  Sylvester’s theorem on partitions is a result in number theory that provides a systematic way to count integer partitions subject to certain congruence or restriction conditions, forming part of the foundational work in partition theory.
• D. Sylvester determinant
  The Sylvester determinant is a mathematical construct introduced by James Joseph Sylvester, typically referring to a determinant associated with resultants and elimination theory in algebra.
• E. Szekeres–Lindström theorem
  The Szekeres–Lindström theorem is a result in combinatorics that characterizes the maximum size of intersecting families of subsets, serving as a precursor to and special case of the Erdős–Ko–Rado theorem.
• F. None of above. chosen