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• W3098864339 abstract "We define the emph{visual complexity} of a plane graph drawing to be the number of basic geometric objects needed to represent all its edges. In particular, one object may represent multiple edges (e.g., one needs only one line segment to draw a path with an arbitrary number of edges). Let $n$ denote the number of vertices of a graph. We show that trees can be drawn with $3n/4$ straight-line segments on a polynomial grid, and with $n/2$ straight-line segments on a quasi-polynomial grid. Further, we present an algorithm for drawing planar 3-trees with $(8n-17)/3$ segments on an $O(n)times O(n^2)$ grid. This algorithm can also be used with a small modification to draw maximal outerplanar graphs with $3n/2$ edges on an $O(n)times O(n^2)$ grid. We also study the problem of drawing maximal planar graphs with circular arcs and provide an algorithm to draw such graphs using only $(5n - 11)/3$ arcs. This is significantly smaller than the lower bound of $2n$ for line segments for a nontrivial graph class." @default.
• W3098864339 created "2020-11-23" @default.
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• W3098864339 date "2018-01-01" @default.
• W3098864339 modified "2023-09-24" @default.
• W3098864339 title "Drawing Planar Graphs with Few Geometric Primitives" @default.
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• W3098864339 doi "https://doi.org/10.7155/jgaa.00473" @default.
• W3098864339 hasPublicationYear "2018" @default.
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