  In this paper a greedy algorithm to detect conflict cliques in interval
graphs and circular-arc graphs is analyzed. In a graph, a stable set requires
that at most one vertex is chosen for each edge. It is equivalent to requiring
that at most one vertex for each maximal clique is chosen. We show that this
algorithm finds all maximal cliques for interval graphs, i.e. it can compute
the convex hull of the stable set polytope. In case of circular-arc graphs, the
algorithm is not able to detect all maximal cliques, yet remaining correct.
This problem occurs in the context of railway scheduling. A train requests the
allocation of a railway infrastructure resource for a specific time interval.
As one is looking for conflict-free train schedules, the used resource
allocation intervals in a schedule must not overlap. The conflict-free choices
of used intervals for each resource correspond to stable sets in the interval
graph associated to the allocation time intervals.
