It is not your sidewalk...
It is where I live.
Each jurisdiction has its own peculiarities regarding ROW and easement laws. In Texas, simply setting aside a strip of land without a formal dedication for use by the general public can establish a public ROW.
Textbook Example:
"The Philmores owned a residence approximately one block from an elementary school in a heavily populated district of a city. There were no sidewalks in the neighborhood. A heavy concentration of children traversed the area twice daily going to and coming from school. To help relieve some of the danger of having the children travel on the side of the street, the Philmores constructed a sidewalk on their property. The children began using the sidewalk, but the Philmores failed to anticipate the adverse effects. The children caused the family dog to bark, the paper was generally missing each morning and minor acts of vandalism occurred on their property. The Philmores finally decided to dismantle the sidewalk. However, they were served with a restraining order by the city attorney’s office. The city contended that the Philmores had granted the public an irrevocable easement across the land."