# Further Maths - Hamiltonian Cycles

> Source: https://ollybritton.com/notes/a-level/further-maths/topics/hamiltonian-cycles/ · Updated: 2021-11-04 · Tags: further-maths, year-2, decision, school

## See Also
## Flashcards
##### What is a Hamiltonian cycle??
A cycle that visits all the vertices of a graph.

##### How many times should a Hamiltonian cycle visit a vertex??
Just one, apart from at the end.

##### What must be true about the start and end vertex of a Hamiltonian cycle??
It must be the same.

##### What is the formula for the number of Hamiltonian cycles for a complete graph $K_n$??
$$
\frac{(n - 1)!}{2}
$$

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