my @E = ([1,3],[1,5],[2,3],[2,4],[2,5],[4,5]);
my $V = 5;
my $verbose = 1;

my @all_edges = map { my $x = $_; map { [$x, $_] } $x+1 .. $V } 1 .. $V-1;

my $string = (join(' ', 1 .. $V) . "\n") x $V
           . "\n"
           . (join(' ', map { join "-", @$_ } @all_edges ) . "\n")
               x @all_edges
           . "\n"
           . (join(' ', map { join "-", @$_ } @E ) . "\n") x $V;

my $regex = "^ "
          . ".* \\b (\\d+) \\b .* \\n\n" x $V
          . "\\n\n"
          . join("", map { my ($x, $y) = @$_;
                           ".* \\b (?: \\$x-\\$y | \\$y-\\$x ) \\b .* \\n\n"
                         } @all_edges)
          . "\\n\n"
          . join("", map { my ($x, $y) = ($_, $_+1);
                           ".* \\b (?: \\$x-\\$y | \\$y-\\$x ) \\b .* \\n\n"
                         } 1 .. ($V-1))
          . ".* \\b (?: \\$V-\\1 | \\1-\\$V ) \\b .* \\n \$\n";

print "'$string' =~ /\n$regex\n/x\n" if $verbose;

if (my @c = $string =~ /$regex/x) {
  local $" = " -> ";
  print "Hamiltonian circuit: [ @c -> $1 ]\n";
} else {
  print "No Hamiltonian circuit\n";
}