On Turn-Regular Orthogonal Representations

An interesting class of orthogonal representations consists the so-called turn-regular ones, i.e., those that do not contain any pair reflex corners point to each other inside a face. For such representation H it is possible compute in linear time minimum-area drawing, drawing minimum area over all assignments vertex and bend coordinates H. In contrast, finding NP-hard if non-turn-regular. This scenario naturally motivates study which graphs admit representations. this paper we identify notable classes biconnected planar always representations, can be computed time. We also describe linear-time testing algorithm for trees provide polynomial-time tests whether plane graph with small faces has without bends.