Irredundancy in multiple interval representations

Abstract In a multiple interval intersection representation of a graph it is required that at least one interval from each of a pair of adjacent vertices intersect. It is permitted for there to be several such intersections, even though these additional intersections are ‘superflous’ or ‘redundant’. By disallowing such redundancies one arrives at the concept of an irredundant multiple interval representation. We show that these irredundant representations can be much more inefficient than representations which allow redundancies. Finally, we show that even when some redundancy is permitted, the inefficiency remains.