NZ Level 7 (NZC) Level 2 (NCEA)
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Hamiltonian Paths and Cycles

Interactive practice questions

Which of the following correctly describes a Hamiltonian cycle?

A cycle that passes through every vertex and every edge exactly once.

A

A path that visits every vertex exactly once.

B

A cycle that passes through every edge exactly once.

C

A path that begins and ends at the same vertex and passes through every other vertex exactly once.

D

A cycle that passes through every vertex and every edge exactly once.

A

A path that visits every vertex exactly once.

B

A cycle that passes through every edge exactly once.

C

A path that begins and ends at the same vertex and passes through every other vertex exactly once.

D
Easy
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The following questions relate to complete graphs.

What is an optimal solution of the traveling salesman problem for a weighted graph?

Is it possible to draw a Hamiltonian path on the following diagram?

Outcomes

M7-5

Choose appropriate networks to find optimal solutions

91260

Apply network methods in solving problems

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