Hello ragnarokPP, and welcome to the Monastery!

tobyink has shown you how to solve the problem with recursion, as you requested. Here is a non-recursive solution using the CPAN module Set::Scalar:

#! perl
use Modern::Perl;
use Set::Scalar;

my $class_callback = sub { join(' ', sort { $a <=> $b } $_[0]->element
+s) };
Set::Scalar->as_string_callback($class_callback);

my @sets;

for (my $i = 0; <DATA>;)
{
    chomp;
    my $new_set = Set::Scalar->new(split /\s+/);
    my $merged  = 0;

    for my $j (0 .. $i - 1)
    {
        if ($new_set->intersection($sets[$j]))
        {
            $sets[$j] = $sets[$j]->union($new_set);
            $merged   = 1;
            last;
        }
    }

    $sets[$i++] = $new_set unless $merged;
}

print '(', $_, ")\n" for @sets;

__DATA__
1 2 4 
2 3 4
3 7
4 6
5 10 11 12 13
6
7 1
[download]

Output:

 1:30 >perl 424_SoPW.pl
(1 2 3 4 6 7)
(5 10 11 12 13)

 1:34 >
[download]

Remember, the Perl motto is TMTOWTDI (There’s More Than One Way To Do It)!

Update: The above code doesn’t merge fully on certain types of input. The following code fixes this:

#! perl
use Modern::Perl;
use Set::Scalar;

my $class_callback = sub { join(' ', sort { $a <=> $b } $_[0]->element
+s) };
Set::Scalar->as_string_callback($class_callback);

my @sets;

for (my $i = 0; <DATA>; ++$i)
{
    chomp;
    $sets[$i] = Set::Scalar->new(split /\s+/);
}

print "Before merging:\n";
print '(', $_, ")\n" for @sets;
print "\n";

for my $i (reverse 1 .. $#sets)
{
    for my $j (0 .. $i - 1)
    {
        if (defined $sets[$i] &&
            defined $sets[$j] &&
            $sets[$i]->intersection($sets[$j]))
        {
            $sets[$j] = $sets[$i]->union($sets[$j]);
            $sets[$i] = undef;
        }
    }
}

@sets = grep { defined } @sets;

print "After merging:\n";
print '(', $_, ")\n" for @sets;

__DATA__
1 2 4
7 13
3 5 6
7 8
10 11 12
1 5
[download]

Output:

11:24 >perl 424_SoPW.pl
Before merging:
(1 2 4)
(7 13)
(3 5 6)
(7 8)
(10 11 12)
(1 5)

After merging:
(1 2 3 4 5 6)
(7 8 13)
(10 11 12)

12:17 >
[download]

Hope that helps,