Drawing slicing graphs with face areas

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Abstract

We consider orthogonal drawings of a plane graph G with specified face areas. For a natural number k, a k-gonal drawing of G is an orthogonal drawing such that the boundary of G is drawn as a rectangle and each inner face is drawn as a polygon with at most k corners whose area is equal to the specified value. In this paper, we show that every slicing graph G with a slicing tree T and a set of specified face areas admits a 10-gonal drawing D such that the boundary of each slicing subgraph that appears in T is also drawn as a polygon with at most 10 corners. Such a drawing D can be found in linear time.

Keywords

Graph algorithms
Graph drawing
Orthogonal drawing
Plane graphs
Slicing graphs

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This research was partially supported by the Scientific Grant-in-Aid from Ministry of Education, Culture, Sports, Science and Technology of Japan.