Theoretical results on at most 1-bend embeddability of graphs

Abstract

1. Introduction Let κ be a non-negative integer. A κ-bend graph is a plane graph in which every edgeis a broken line consisting of at most κ+ 1 horizontal or vertical segments. A bend is any point which is the intersection of a horizontal segment and a verticalsegment of an edge. A planar graph G is κ-rectilinear if it admits a plane embedding Gwhich is a κ-bend graph. In this case G is said to be a κ-embedding of G.