König's theorem in graph theory

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

• A. 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.
• B. Pósa’s theorem in graph theory
  Pósa’s theorem in graph theory is a result that gives a sufficient degree condition for a finite graph to contain a Hamiltonian cycle.
• C. 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.
• D. Gallai theorem
  Gallai's theorem is a fundamental result in graph theory and Ramsey theory that characterizes the structure of colorings of complete graphs by guaranteeing large monochromatic or well-organized subgraphs.
• E. Turán's theorem
  Turán's theorem is a fundamental result in extremal graph theory that determines the maximum number of edges a graph can have without containing a complete subgraph of a given size.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: König's theorem in graph theory
Target entity description: König's theorem in graph theory is a fundamental result in bipartite graphs stating that the size of a maximum matching equals the size of a minimum vertex cover.

• A. 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.
• B. Pósa’s theorem in graph theory
  Pósa’s theorem in graph theory is a result that gives a sufficient degree condition for a finite graph to contain a Hamiltonian cycle.
• C. 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.
• D. Gallai theorem
  Gallai's theorem is a fundamental result in graph theory and Ramsey theory that characterizes the structure of colorings of complete graphs by guaranteeing large monochromatic or well-organized subgraphs.
• E. Turán's theorem
  Turán's theorem is a fundamental result in extremal graph theory that determines the maximum number of edges a graph can have without containing a complete subgraph of a given size.
• F. None of above. chosen