Theoretical results on at most 1-bend embeddability of graphs (original) (raw)

This study investigates the concept of 1-rectilinear graphs, emphasizing their embedding within the plane using at most one bend. The paper characterizes 1-rectilinear graphs based on certain forbidden subgraphs and introduces a polynomial-time algorithm to determine the existence of a 1-embedding for a given graph. Furthermore, it establishes upper bounds on the total number of bends for various classes of graphs, providing significant insights into the embedding capabilities of planar graphs with respect to bends.