Graph implications

Discrete Mathematics Level 4

If a graph is simple and hypohamiltonian, which of these statements must be true?

A. It is hamiltonian
B. It is nonplanar
C. It is 3-connected

A simple graph has no loops or multiple edges.
A hamiltonian cycle of a graph is a cycle that goes through all vertices of the graph.
A graph is hamiltonian if it has a hamiltonian cycle.
A graph is hypohamiltonian if it has at least two vertices, and removing any one vertex of the graph leaves it hamiltonian.
A graph is 3-connected if it has at least four vertices, and removing any two vertices from the graph still leaves it connected.
A graph is planar if it can be drawn on the plane without any two edges crossing.
A graph is nonplanar if it is not planar.


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