König's lemma in infinite graph theory

Target entity: König's lemma in infinite graph theory
Context triple: [Julius König, knownFor, König's lemma in infinite graph theory]

• A. Kruskal's tree theorem
  Kruskal's tree theorem is a fundamental result in combinatorics and mathematical logic stating that finite trees are well-quasi-ordered under homeomorphic embedding, with deep implications in proof theory and computer science.
• B. Ky Fan’s lemma
  Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
• C. Menger theorem in graph theory
  Menger's theorem in graph theory is a fundamental result that characterizes the connectivity between two vertices in a graph by equating the maximum number of pairwise internally disjoint paths between them with the minimum size of a vertex cut separating them.
• D. Tarski’s fixed point theorem
  Tarski’s fixed point theorem is a fundamental result in order theory and lattice theory that guarantees the existence of fixed points for monotone functions on complete lattices, with wide applications in logic, computer science, and economics.
• E. 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.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: König's lemma in infinite graph theory
Target entity description: König's lemma in infinite graph theory is a fundamental result stating that every infinite, finitely branching tree contains an infinite path.

• A. Kruskal's tree theorem
  Kruskal's tree theorem is a fundamental result in combinatorics and mathematical logic stating that finite trees are well-quasi-ordered under homeomorphic embedding, with deep implications in proof theory and computer science.
• B. Ky Fan’s lemma
  Ky Fan’s lemma is a combinatorial topological result that generalizes Tucker’s lemma and provides conditions guaranteeing the existence of certain balanced or fully labeled simplices in labeled triangulations of spheres or simplices.
• C. Menger theorem in graph theory
  Menger's theorem in graph theory is a fundamental result that characterizes the connectivity between two vertices in a graph by equating the maximum number of pairwise internally disjoint paths between them with the minimum size of a vertex cut separating them.
• D. Tarski’s fixed point theorem
  Tarski’s fixed point theorem is a fundamental result in order theory and lattice theory that guarantees the existence of fixed points for monotone functions on complete lattices, with wide applications in logic, computer science, and economics.
• E. 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.
• F. None of above. chosen