Hexagonal grid drawings

Abstract

In this paper we present a linear algorithm to draw tricounected planar graphs of degree 3 planar on a linear-sized hexagonal grid such that in at most one edge are bends. This algorithm can be used to draw this class of graphs planar with straight lines on a n/2 × n/2 grid, improving the best known grid bounds by a factor 4. We also show how to draw planar graphs of degree at most 3 planar with straight lines such that the minimum angle is ≥ π/6, thereby answering a question of Formaun et al.