GD 2004: Graph Drawing pp 111-121

# Unit Bar-Visibility Layouts of Triangulated Polygons

• Alice M. Dean
• Ellen Gethner
• Joan P. Hutchinson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3383)

## Abstract

A triangulated polygon is a 2-connected maximal outerplanar graph. A unit bar-visibility graph (UBVG for short) is a graph whose vertices can be represented by disjoint, horizontal, unit-length bars in the plane so that two vertices are adjacent if and only if there is a non-degenerate, unobstructed, vertical band of visibility between the corresponding bars. We give combinatorial and geometric characterizations of the triangulated polygons that are UBVGs. To each triangulated polygon G we assign a character string with the property that G is a UBVG if and only if the string satisfies a certain regular expression. Given a string that satisfies this condition, we describe a linear-time algorithm that uses it to produce a UBV layout of G.

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## Authors and Affiliations

• Alice M. Dean
• 1
• Ellen Gethner
• 2
• Joan P. Hutchinson
• 3
1. 1.Skidmore CollegeSaratoga SpringsUSA
2. 2.University of Colorado at DenverDenverUSA
3. 3.Macalester CollegeSt. PaulUSA