Upon a petition signed by the owners of a majority of the frontage of the lots fronting upon a street, the planting, care and maintenance of which has been assumed by the City, being filed with the City Clerk petitioning that the planting, care and maintenance terminate, the City Council shall fix a time and place for the hearing of the petition and cause notice thereof to be given by publication for five days in a newspaper published and circulated in the City. The time of hearing shall be not less than fifteen days from the date of the first publication of the notice. At such hearing the City Council may, in its discretion, order the abandonment of all further planting, care and maintenance of such grass, shrubbery and trees assumed as provided in this chapter and may fix a time at which such planting, care and maintenance by the City shall cease. (Code 1962, § 35-34)