# Finding and displaying Hamiltonian cycles in Matgraph

We illustrate how to find a Hamiltonian cycle in a graph, convert that cycle into a subgraph, and then display the results.

## Create a graph and find a Hamiltonian cycle

For this illustration, we use the dodecahedron graph.

Note: The dodecahedron graph comes with a built-in embedding. We use this embedding later when we draw the graph and its Hamiltonian cycle.

```g = graph;
dodecahedron(g);
c = hamiltonian_cycle(g);
disp(c')
```
```  Columns 1 through 14

1     2     3     4     5    10    14     9    13     8    12     7    11    16

Columns 15 through 20

17    18    19    20    15     6

```

## Convert the list of vertices into a cycle graph

```n = nv(g);
h = graph(n);
for k=1:n-1
end
```

## Copy the embedding of the original graph to the cycle

```embed(h, getxy(g))
```

## Create the drawing

We first draw g with dotted lines and then overlay the result with h drawn with solid lines.

```draw(g,':')
draw(h)
```

## Release graphs

```free(g)
free(h)
```