If you want to ensure your image sizes remain available when switching themes, then you should place them into a plugin. Create a .php file (name it what you want) and place it in wp-content/plugins/, then paste the following:
<?php
/*
Plugin Name: My Custom Image Sizes
Plugin URI: http://pippinsplugins.com/
Description: Images sizes to be used in all themes
Author: Pippin Williamson
Author URI: http://pippinsplugins.com
Version: 1.0
*/
add_image_size('thumb' , 130, 65, true ); // Thumb
add_image_size('max' , 610, 305, true ); // Maximum
add_image_size('min' , 270, 135, true ); // Minimum
Once you activate the plugin, your image sizes will be available no matter what theme is activated.