Rectangle and Square Representations of Planar Graphs

摘要: In the first part of this survey, we consider planar graphs that can be represented by a dissections rectangle into rectangles. rectangular drawings, corners rectangles represent vertices. The graph obtained taking as vertices and contacts edges is dual. visibility segment contact graphs, correspond to horizontal or vertical segments dissection. Special orientations turn out helpful when dealing with characterization representation questions. Therefore, look at prescribed degrees, bipolar orientations, separating decompositions, transversal structures.