In advertising for bids for paving, repaving, graveling, or macadamizing, the mayor and city council may provide for bids on different materials and types of construction, and shall in addition provide for asking bids on any material or materials that may be suggested by petition of owners of the record title representing twenty-five percent of the abutting property owners in an improvement district, if such petition is filed with the city clerk before advertisement for bids is ordered. On opening of bids for paving or repaving in any such district, the mayor and city council shall postpone action thereon for a period of not less than ten days. During such period of postponement, the owners of the record title representing a majority of the abutting property owners in a district may file with the city clerk a petition for the use of a particular material for paving for which a bid has been received, in which event a bid on that material shall be accepted and the work shall be done with that material. The regulations as to advertising for bids and opening of bids and postponing of action thereon and the right of selection of materials shall not apply in case of graveling. In case such owners fail to designate the material they desire used in such paving or repaving, or macadamizing, in the manner and within the time provided in this section, the mayor and city council shall determine the material to be used. The mayor and city council may reject all bids and readvertise if, in their judgment, the public interest requires.