A monotone drawing of a planar graph G is a planar straight-line drawing of G where a monotone path exists between every pair of vertices of G in some direction. Recently monotone drawings of planar graphs have been proposed as a new standard for visualizing graphs. A monotone drawing of a planar graph is a monotone grid drawing if every vertex in the drawing is drawn on a grid point. In this paper we study monotone grid drawings of planar graphs in a variable embedding setting. We show that every connected planar graph of n vertices has a monotone grid drawing on a grid of size O(n)times;O(n 2), and such a drawing can be found in O(n) time. Our result immediately resolves two open problems on monotone drawings of planar graphs posted by Angelini et al. © 2014 Springer International Publishing.
CITATION STYLE
Hossain, M. I., & Rahman, M. S. (2014). Monotone grid drawings of planar graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8497 LNCS, pp. 105–116). Springer Verlag. https://doi.org/10.1007/978-3-319-08016-1_10
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