Compact drawings of 1-planar graphs with right-angle crossings and few bends

摘要

We study the following classes of beyond-planar graphs: 1-planar, IC-planar, and NIC-planar graphs. These are the graphs that admit a 1-planar, IC-planar, and NIC-planar drawing, respectively. A drawing of a graph is 1-planar if every edge is crossed at most once. A 1-planar drawing is IC-planar if no two pairs of crossing edges share a vertex, A 1-planar drawing is NIC-planar if no two pairs of crossing edges share two vertices.