by Stephen Harris14 May 2012
url:https://code.tutsplus.com/tutorials/understanding-the-walker-class--wp-25401

class SH_Child_Only_Walker extends Walker_Nav_Menu {
 
    // Don't start the top level
    function start_lvl(&$output, $depth=0, $args=array()) {
        if( 0 == $depth )
            return;
        parent::start_lvl(&$output, $depth,$args);
    }
 
    // Don't end the top level
    function end_lvl(&$output, $depth=0, $args=array()) {
        if( 0 == $depth )
            return;
        parent::end_lvl(&$output, $depth,$args);
    }
 
    // Don't print top-level elements
    function start_el(&$output, $item, $depth=0, $args=array()) {
        if( 0 == $depth )
            return;
        parent::start_el(&$output, $item, $depth, $args);
    }
 
    function end_el(&$output, $item, $depth=0, $args=array()) {
        if( 0 == $depth )
            return;
        parent::end_el(&$output, $item, $depth, $args);
    }
 
    // Only follow down one branch
    function display_element( $element, &$children_elements, $max_depth, $depth=0, $args, &$output ) {
 
        // Check if element as a 'current element' class
        $current_element_markers = array( 'current-menu-item', 'current-menu-parent', 'current-menu-ancestor' );
        $current_class = array_intersect( $current_element_markers, $element->classes );
 
        // If element has a 'current' class, it is an ancestor of the current element
        $ancestor_of_current = !empty($current_class);
 
        // If this is a top-level link and not the current, or ancestor of the current menu item - stop here.
        if ( 0 == $depth && !$ancestor_of_current)
            return
 
        parent::display_element( $element, &$children_elements, $max_depth, $depth, $args, &$output );
    }
}