Lecture Notes in Computer Science Volume 3383, 2005, pp 18-24

Hexagonal Grid Drawings: Algorithms and Lower Bounds

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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 K 7, and give asymptotic lower bounds for graph classes of varying connectivity.