Before revision:  De Luca et al. [GD'18] considered the recognition problem of stick graphs for the case that the ordering of either one of the two sets  (STICK_A) is given and for the case that the ordering of both sets is given (STICK_AB).
After revision:  De Luca et al. [GD'18] considered the recognition problem of stick graphs for the case that the ordering of either one of the two sets (STICK_A) , and when the order of both sets is given (STICK_AB).