Hexagonal grid drawings: Algorithms and lower bounds

Abstract

We study drawings of graphs of maximum degree six on the hexagonal (triangular) grid, with the main focus of keeping the number of bends small. We give algorithms that achieve 3.5n + 3.5 bends for all simple graphs. We also prove optimal lower bounds on the number of bends for K7, and give asymptotic lower bounds for graph classes of varying connectivity. © Springer-Verlag Berlin Heidelberg 2004.