If a sidewalk or curb has not been constructed, or if a defective sidewalk or curb has not been reconstructed, repaired or freed from nuisance, within the period of time permitted by the notice to the owner of the abutting property, the Engineer shall prepare a list of such sidewalks and curbs and present it to Council, which shall proceed, as provided in Ohio R.C. 729.01 to 729.11, inclusive, to cause the necessary construction to be made and to assess the entire cost against the abutting property.