Dirac's theorem

Dirac's theorem may refer to:

• Dirac's theorem on Hamiltonian cycles, the statement that an n-vertex graph in which each vertex has degree at least n/2 must have a Hamiltonian cycle
• Dirac's theorem on chordal graphs, the characterization of chordal graphs as graphs in which all minimal separators are cliques
• Dirac's theorem on cycles in k-connected graphs, the result that for every set of k vertices in a k-vertex-connected graph there exists a cycle that passes through all the vertices in the set

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