Area, perimeter, height, and width of rectangle visibility graphs

John S. Caughman (), Charles L. Dunn (), Joshua D. Laison (), Nancy Ann Neudauer () and Colin L. Starr ()
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John S. Caughman: Portland State University
Charles L. Dunn: Linfield University
Joshua D. Laison: Willamette University
Nancy Ann Neudauer: Pacific University
Colin L. Starr: Willamette University

Journal of Combinatorial Optimization, 2023, vol. 46, issue 3, No 1, 22 pages

Abstract: Abstract A rectangle visibility graph (RVG) is represented by assigning to each vertex a rectangle in the plane with horizontal and vertical sides in such a way that edges in the graph correspond to unobstructed horizontal and vertical lines of sight between their corresponding rectangles. To discretize, we consider only rectangles whose corners have integer coordinates. For any given RVG, we seek a representation with smallest bounding box as measured by its area, perimeter, height, or width (height is assumed not to exceed width). We derive a number of results regarding these parameters. Using these results, we show that these four measures are distinct, in the sense that there exist graphs $$G_1$$ G 1 and $$G_2$$ G 2 with $${{\,\textrm{area}\,}}(G_1)

Keywords: Visibility graph; Rectangle visibility graph; Bar visibility graph; 05C62 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10878-023-01084-9

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