On the $2$-Bend Slope Number of $1$-Planar Graphs

Abstract

While drawing planar graphs with few slopes and few bends is a well-studied problem, corresponding extensions to beyond-planar graphs still remain mostly unexplored. Motivated by this observation, in this work, we provide bounds on the slope number of biconnected $1$-planar graphs when two bends are allowed along each edge. Our contribution is an incremental drawing algorithm that produces $2$-bend $1$-planar drawings of biconnected $1$-plane graphs with maximum degree $\Delta$ using any prescribed set of $\Delta$ pairwise distinct slopes.

A preliminary version of this work was published at GD 2026