  We consider a variant of the crash-fault gathering problem called stand-up
indulgent gathering (SUIG). In this problem, a group of mobile robots must
eventually gather at a single location, which is not known in advance. If no
robots crash, they must all meet at the same location. However, if one or more
robots crash at a single location, all non-crashed robots must eventually
gather at that location. The SUIG problem was first introduced for robots
operating in a two-dimensional continuous Euclidean space, with most solutions
relying on the ability of robots to move a prescribed (real) distance at each
time instant. In this paper, we investigate the SUIG problem for robots
operating in a discrete universe (i.e., a graph) where they can only move one
unit of distance (i.e., to an adjacent node) at each time instant.
Specifically, we focus on line-shaped networks and characterize the solvability
of the SUIG problem for oblivious robots without multiplicity detection.
