Dirac's theorem about Hamiltonian graphs | graph theory

5 months ago
43
Science mathematics graph graph theory combinatorics discrete mathematics Hamiltonian Hamiltonian graph Hamiltonian cycle cycle path

Episode 44.

Dirac's theorem about Hamiltonian graphs | graph theory.

Definition. A Hamiltonian cycle in a graph is a cycle that passes through all vertices of the graph.
Definition. A graph is said to be Hamiltonian if it has a Hamiltonian cycle.
Dirac's theorem. For any graph $G$ on $n$ vertices, where $n \geq 3$, if the degree of any vertex is greater or equal than $n/2$, then the graph $G$ is Hamiltonian.

Mathematics. Discrete Mathematics. Combinatorics. Graph theory.
#Mathematics #DiscreteMathematics #Combinatorics #GraphTheory

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