$ perl graph.pl 3
    5 6 9
 
    $ perl graph.pl 4
    1 2 3 4

##</code><code>##

 
$ perl graph.pl 3
would give:
 
1 2 3
1 2 4
1 3 4
2 3 4
5 6 9

##</code><code>##

_BEGIN__
#Credit Greg Bacon
#and suggestion by C.Clarkson

my @vertices = 1 .. 9;
my @edges = (
    [1,2], [1,3], [1,4], [1,5],
    [2,3], [2,4],
    [3,4],
    [5,6], [5,7], [5,9],
    [6,9],
    [7,8],
    [8,9],
);

       $k = shift || 3;
 
    #Construct a string as follows:
 
        $string = (join ',' => @V) .  ';'
                . (join ',' => map "$_->[0]-$_->[1]", @E);
 
    #Then construct a regular expression as follows:
 
        $regex = '^ .*\b '
               . join(' , .*\b ' => ('(\d+)') x $k)
               . '\b .* ;'
               . "\n";
 
        for ($i = 1; $i < $k; $i++) {
            for ($j = $i+1; $j <= $k; $j++) {
                $regex .= '(?= .* \b ' . "\\$i-\\$j" . ' \b)' . "\n";
            }
        }
 
    #Our graph contains a k-clique if and only if
 
        if ($string =~ /$regex/x) {
            print join(" ", map $$_, 1..$k), "\n";
        }
__END__