Combinatorial Properties of TriangleFree Rectangle Arrangements and the Squarability ProblemKlawitter, Jonathan and Nöllenburg, Martin and Ueckerdt, Torsten (2015) Combinatorial Properties of TriangleFree Rectangle Arrangements and the Squarability Problem. In: Graph Drawing and Network Visualization: 23rd International Symposium, GD 2015, September 2426, 2015 , pp. 231244(Official URL: http://dx.doi.org/10.1007/9783319272610_20). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/9783319272610_20
AbstractWe consider arrangements of axisaligned rectangles in the plane. A geometric arrangement specifies the coordinates of all rectangles, while a combinatorial arrangement specifies only the respective intersection type in which each pair of rectangles intersects. First, we investigate combinatorial contact arrangements, i.e., arrangements of interiordisjoint rectangles, with a trianglefree intersection graph. We show that such rectangle arrangements are in bijection with the 4orientations of an underlying planar multigraph and prove that there is a corresponding geometric rectangle contact arrangement. Using this, we give a new proof that every trianglefree planar graph is the contact graph of such an arrangement. Secondly, we introduce the question whether a given rectangle arrangement has a combinatorially equivalent square arrangement. In addition to some necessary conditions and counterexamples, we show that rectangle arrangements pierced by a horizontal line are squarable under certain sufficient conditions.
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