  This paper focuses on a variation of the Art Gallery problem that considers
open edge guards and open mobile guards. A mobile guard can be placed on edges
and diagonals of a polygon, and the "open" prefix means that the endpoints of
such edge or diagonal are not taken into account for visibility purposes. This
paper studies the number of guards that are sufficient and sometimes necessary
to guard some classes of simple polygons for both open edge and open mobile
guards. This problem is also considered for planar triangulation graphs using
open edge guards.
