On rectangle visibility graphs

  • Prosenjit Bose
  • Alice Dean
  • Joan Hutchinson
  • Thomas Shermer
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1190)

Abstract

We study the problem of drawing a graph in the plane so that the vertices of the graph are rectangles that are aligned with the axes, and the edges of the graph are horizontal or vertical lines-of-sight. Such a drawing is useful, for example, when the vertices of the graph contain information that we wish displayed on the drawing; it is natural to write this information inside the rectangle corresponding to the vertex. We call a graph that can be drawn in this fashion a rectangle-visibility graph, or RVG. Our goal is to find classes of graphs that are RVGs. We obtain several results:
  1. 1.

    For 1 ≤ k ≤ 4, k-trees are RVGs.

     
  2. 2.

    Any graph that can be decomposed into two caterpillar forests is an RVG.

     
  3. 3.

    Any graph whose vertices of degree four or more form a distance-two independent set is an RVG.

     
  4. 4.

    Any graph with maximum degree four is an RVG. Our proofs are constructive and yield linear-time layout algorithms.

     

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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Prosenjit Bose
    • 1
  • Alice Dean
    • 2
  • Joan Hutchinson
    • 3
  • Thomas Shermer
    • 4
  1. 1.Université du Québec à Trois-RivièresCanada
  2. 2.Skidmore CollegeUSA
  3. 3.Macalester CollegeUSA
  4. 4.Simon Fraser UniversityCanada

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