These water-soluble markers work well with Role Playing Game vinyl mats. The black, blue, and green colors are the are the easiest to remove with water. The red has a tendency of staining much more than the other colors so it is best used for highlighting only. 

NOTE: Never use dry erase, permanent, or grease-pencil markers. The vinyl is too porous for the lines created from them to be able to be removed. If you have any doubt of the suitability of any particular marker, draw a small line on the border, let sit for a while, and see how well it can be removed. Better to have a small permanent blemish on the edge of the mat than a permanent map drawn on the entirety of the mat.