The visual complexity of a plane graph drawing is defined 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 pathwith an arbitrary number of edges). A crossing-free straight-line drawing of a graph is called monotone if there is a monotone path between any pair of vertices with respect to some direction. We study drawings of trees, outerplanar graphs, and general planar graphs with few segments on a polynomial size grid. For trees , the grid size is n\times n. For 3-connected planar graphs and biconnected outerplanar graphs , we compute such drawings that are also monotone .
The visual complexity of a graph drawing can be measured by the number of geometric objects used for the representation of its elements. In this paper, we study planar graph drawings where edges are represented by few segments. In such a drawing, one segment may represent multiple edges forming a path. Drawings of planar graphs with few segments were intensively studied in the past years. However, the area requirements were only considered for limited subclasses of planar graphs. In this paper, we show that trees have drawings with 3n/4-1 segments and n^2 area, improving the previous result of O(n^{3.58 3-connected planar graphs and biconnected outerplanar graphs have a drawing with 8n/3-O(1) and 3n/2-O(1) segments, respectively, and O(n^3) area .
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plane graph drawing is defined to be
graph drawing can be measured by
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basic geometric objects needed to represent all its edges. In particular, one object
geometric objects used for the representation of its elements. In this paper, we study planar graph drawings where edges are represented by few segments. In such a drawing, one segment
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(e.g., one needs only one line segment to draw a pathwith an arbitrary number of edges). A crossing-free straight-line drawing of a graph is called monotone if there is a monotone path between any pair of vertices with respect to some direction. We study drawings of trees, outerplanar graphs, and general
forming a path. Drawings of
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on a polynomial size grid. For trees , the grid size is n\times n. For
were intensively studied in the past years. However, the area requirements were only considered for limited subclasses of planar graphs. In this paper, we show that trees have drawings with 3n/4-1 segments and n^2 area, improving the previous result of O(n^{3.58
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, we compute such drawings that are also monotone
have a drawing with 8n/3-O(1) and 3n/2-O(1) segments, respectively, and O(n^3) area