category / child category conditional

I am designing my category.php file. I would like to link to different CSS files depending on what category the post is assigned to. Basically, if a post if from category 1 or a child category of 1 I would like to link to cat1.css and if the post is from category 2 (or child category of 2) I would want to link cat2.css

Below is my code from category-header.php Unfortunately it is not working, it doesn’t display the child categories.

<?php if ( is_category(1) ) {
	echo '<link rel="stylesheet" href="' . get_bloginfo(template_directory) . '/style/css/cat1.css" type="text/css" media="screen" />';
	} else {
	echo '<link rel="stylesheet" href="' . get_bloginfo(template_directory) . '/style/css/cat2.css" type="text/css" media="screen" />'; }

Any help is much appreciated!