At any time after all or a portion of a city street becomes a county highway, as provided in this article, and all improvements commenced by the county, or its agents thereon, have been fully completed, the board of supervisors of such county may adopt a resolution declaring that all or any portion of such street is no longer a county highway. Ten days after the filing of such resolution with the clerk of the city within which the street lies, such street, or the portion thereof described in the resolution, shall cease to be a county highway.