Permalink remain the same on each page

Firstly, you should never use query_posts to construct custom queries. This is not just my emphasis, but the codex as well. The one big problem with query_posts is, it many circumstances, pagination fails

Note: This function isn’t meant to be used by plugins or themes. As explained later, there are better, more performant options to alter the main query. query_posts() is overly simplistic and problematic way to modify main query of a page by replacing it with new instance of the query. It is inefficient (re-runs SQL queries) and will outright fail in some circumstances (especially often when dealing with posts pagination).

You need to construct you custom query with WP_Query.

Take a look at the_title( $before, $after, $echo );. Here are the parameters

$before

(string) (optional) Text to place before the title.

Default: None

$after

(string) (optional) Text to place after the title.

Default: None

$echo

(Boolean) (optional) Display the title (TRUE) or return it for use in PHP (FALSE).

Default: TRUE

So you can simply just do something like this

the_title( '<a href="' . esc_url( get_permalink() ) . '" rel="bookmark">', '</a>' );

You query should then look like this with all the before said. Before I forget, showposts has long time been depreciated, it was replaced with posts_per_page. If you had debug set to true in wp-config, you should have received a depreciation notice in the front end that would have indicated this. Read here: Debugging WordPress

<?php
$args = array(
   'cat' => 4,
   'posts_per_page' => 1
);
// The Query
$the_query = new WP_Query( $args );

// The Loop
if ( $the_query->have_posts() ) {
    echo '<ul>';
    while ( $the_query->have_posts() ) {
        $the_query->the_post();
        the_title( '<a href="' . esc_url( get_permalink() ) . '" rel="bookmark">', '</a>' );
    }
    echo '</ul>';
} else {
    // no posts found
}
/* Restore original Post Data */
wp_reset_postdata();

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