```
# NOT RUN {
## Dodekaeder graph
D20_edges <- c(
1, 2, 1, 5, 1, 6, 2, 3, 2, 8, 3, 4, 3, 10, 4, 5, 4, 12,
5, 14, 6, 7, 6, 15, 7, 8, 7, 16, 8, 9, 9, 10, 9, 17, 10, 11,
11, 12, 11, 18, 12, 13, 13, 14, 13, 19, 14, 15, 15, 20, 16, 17, 16, 20,
17, 18, 18, 19, 19, 20)
hamiltonian(D20_edges, cycle = TRUE)
# [1] 1 2 3 4 5 14 13 12 11 10 9 8 7 16 17 18 19 20 15 6
hamiltonian(D20_edges, cycle = FALSE)
# [1] 1 2 3 4 5 14 13 12 11 10 9 8 7 6 15 20 16 17 18 19
## Herschel graph
# The Herschel graph the smallest non-Hamiltonian polyhedral graph.
H11_edges <- c(
1, 2, 1, 8, 1, 9, 1, 10, 2, 3, 2, 11, 3, 4, 3, 9, 4, 5,
4, 11, 5, 6, 5, 9, 5, 10, 6, 7, 6, 11, 7, 8, 7, 10, 8, 11)
hamiltonian(H11_edges, cycle = FALSE)
# NULL
# }
# NOT RUN {
## Example: Graph constructed from squares
N <- 45 # 23, 32, 45
Q <- (2:trunc(sqrt(2*N-1)))^2
sq_edges <- c()
for (i in 1:(N-1)) {
for (j in (i+1):N) {
if ((i+j) <!-- %in% Q) { -->
sq_edges <- c(sq_edges, i, j)
}
}
require(igraph)
sq_graph <- make_graph(sq_edges, directed=FALSE)
plot(sq_graph)
if (N == 23) {
# does not find a path with start=1 ...
hamiltonian(sq_edges, start=18, cycle=FALSE)
# hamiltonian(sq_edges) # NULL
} else if (N == 32) {
# the first of these graphs that is Hamiltonian ...
# hamiltonian(sq_edges, cycle=FALSE)
hamiltonian(sq_edges)
} else if (N == 45) {
# takes much too long ...
# hamiltonian(sq_edges, cycle=FALSE)
hamiltonian(sq_edges)
}
# }
```

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