Display related post from same category only, need some help!

using this code:

function related_posts() {
$args = array(
'tag__in' => $tag_ids,
'post__not_in' => array (get_the_ID()),
'posts_per_page'=>4,
'caller_get_posts'=>1,
'orderby'=>'rand'
);
$the_query = new WP_Query( $args ); 

while ( $the_query->have_posts() ) : $the_query->the_post();
?>

this is running on single pages only, how could i modify the code to only include related posts from the same category as the single post (they are always only in 1 category)

can i use ‘cat_not_in’ => array (‘1′,2′,’3’)), to exclude categories specified by id?