Four-bend necessity conjecture for planar graph EPG representations

An EPG representation of a graph represents each vertex by a path in the square grid, with adjacency corresponding to sharing a grid edge; a path has a bend at each change of grid direction. Four-bend necessity conjecture. There exists a planar graph $G$ such that every EPG representation of $G$ contains at least one path with four bends. The source places this statement in the conclusions alongside the open determination of the maximum bend-number of planar graphs, while its preceding theorem establishes only that this maximum is either three or four.