Rectangle-of-influence drawings of four-connected plane graphs: extended abstract

  • Authors:

  • Kazuyuki Miura;Takao Nishizeki

  • Affiliations:

  • Tohoku University, Sendai, Japan;Tohoku University, Sendai, Japan

  • Venue:
  • APVis '05 proceedings of the 2005 Asia-Pacific symposium on Information visualisation - Volume 45
  • Year:
  • 2005

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Abstract

A rectangle-of-influence drawing of a plane graph G is a straight-line planar drawing of G such that there is no vertex in the proper inside of the axis-parallel rectangle defined by the two ends of any edge. In this paper, we show that any 4-connected plane graph G with four or more vertices on the outer face has a rectangle-of-influence drawing in an integer grid such that W + H ≤ n, where n is the number of vertices in G, W is the width and H is the height of the grid. Thus the area W x H of the grid is at most [(n-1)/2] [(n-1)/2]. Our bounds on the grid sizes are optimal in a sense that there exist an infinite number of 4-connected plane graphs whose drawings need grids such that W + H = n - 1 and W x H = [(n-1)/2]. [(n-1)/2]. We also show that the drawing can be found in linear time.