Combining Problems on RAC Drawings and Simultaneous Graph Drawings

We present an overview of the first combinatorial results for the so-called geometricRACsimultaneousdrawingproblem (or GRacSim drawing problem, for short), i.e., a combination of problems on geometric RAC drawings [3] and geometric simultaneous graph drawings [2]. According to this problem, we are given two planar graphs G1 =(V, E1 ) and G2 =(V, E2 ) that share a common vertex set but have disjoint edge sets, i.e., E1 ⊆V ×V , E2 ⊆V ×V and E1 ∩E2 =∅ The main task is to place the vertices on the plane so that, when the edges are drawn as straight-lines, (i) each graph is drawn planar, (ii) there are no edge overlaps, and, (iii) crossings between edges in E1 and E2 occur at right angles.