A more efficient formulation:

#! perl -slw
use strict;
use Data::Dump qw[ pp ];

my @array = (['A','B'],['C','D'],['A','C'],['E','F'],['F','G']);
my @buckets;

for( sort { $a->[0] cmp $b->[0] } @array ) {
    my( $x, $y ) = @$_;
    my $added = 0;
    for my $bkt ( @buckets ) {
        if( exists $bkt->{ $x } or exists $bkt->{ $y } ) {
            undef @{ $bkt }{ $x, $y };
            ++$added;
        }
    }
    push @buckets, { $x, undef, $y, undef } unless $added;
}
$_ = [ sort keys %$_ ] for @buckets;
pp \@buckets;

__END__
C:\test>1017261-2
[["A", "B", "C", "D"], ["E", "F", "G"]]
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