Drawing slicing graphs with face areas

  • Authors:
  • Akifumi Kawaguchi;Hiroshi Nagamochi

  • Affiliations:
  • Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Japan;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Japan

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2009

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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.