A Hamiltonian graph is biconnected. The converse is not true.

Episode 37.

A Hamiltonian graph is biconnected. The converse is not true.

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.
Definition A graph is said to be biconnected if it is connected and, after a removal of any vertex, it remains connected.
Theorem. A Hamiltonian graph is biconnected. The converse is not true.

Graph theory.
#GraphTheory

The same video on YouTube:
https://youtu.be/g7z1_gvtmaU

The same video on Telegram:
https://t.me/mathematical_bunker/61