Unit Bar-visibility Layouts of Triangulated Polygons: Extended 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 nondegenerate, 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.