# 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.

## Contents

## 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 add(h,c(k),c(k+1)) end add(h,c(1),c(n))

## 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)