Minimum-segment convex drawings of 3-connected cubic plane graphs

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Abstract

A convex drawing of a plane graph G is a plane drawing of G, where each vertex is drawn as a point, each edge is drawn as a straight line segment and each face is drawn as a convex polygon. A maximal segment is a drawing of a maximal set of edges that form a straight line segment. A minimum-segment convex drawing of G is a convex drawing of G where the number of maximal segments is the minimum among all possible convex drawings of G. In this paper, we present a linear-time algorithm to obtain a minimum-segment convex drawing Γ of a 3-connected cubic plane graph G of n vertices, where the drawing is not a grid drawing. We also give a linear-time algorithm to obtain a convex grid drawing of G on an grid with at most s n +1 maximal segments, where is the lower bound on the number of maximal segments in a convex drawing of G. © 2010 Springer-Verlag Berlin Heidelberg.

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APA

Biswas, S., Mondal, D., Nishat, R. I., & Rahman, M. S. (2010). Minimum-segment convex drawings of 3-connected cubic plane graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6196 LNCS, pp. 182–191). https://doi.org/10.1007/978-3-642-14031-0_21

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