Chronological rectangle digraphs which are two-terminal series–parallel

Abstract

Chronological interval digraphs are a natural directed analogue of interval graphs. They admit elegant characterizations as well as efficient recognition algorithms. Recently, a generalization of chronological interval digraphs to 2-dimensional space called chronological rectangle digraphs was introduced and studied. Although many interesting properties of chronological rectangle digraphs have been discovered, the most fundamental question of whether this class of digraphs can be recognized in polynomial-time remains unanswered. This is largely due to the lack of a good structural characterization for the class. In this paper, we study chronological rectangle digraphs which are also two-terminal series–parallel. We show that this restricted class of digraphs admits a forbidden induced subdigraph characterization, which leads to a polynomial-time recognition algorithm for this class of digraphs.