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Intersection graphs of L-shapes and segments in the plane.

Felsner, S. and Knauer, K. and Mertzios, G.B. and Ueckerdt, T. (2016) 'Intersection graphs of L-shapes and segments in the plane.', Discrete applied mathematics., 206 . pp. 48-55.


An L-shape is the union of a horizontal and a vertical segment with a common endpoint. These come in four rotations: Full-size image (25 K), Full-size image (25 K),Full-size image (25 K) and Full-size image (25 K). A k-bend path is a simple path in the plane, whose direction changes k times from horizontal to vertical. If a graph admits an intersection representation in which every vertex is represented by an Full-size image (25 K), an Full-size image (25 K) or Full-size image (25 K), a k-bend path, or a segment, then this graph is called an {Full-size image (25 K)}-graph, {Full-size image (25 K),Full-size image (25 K)}-graph, Bk-VPG-graph or SEG-graph, respectively. Motivated by a theorem of Middendorf and Pfeiffer (1992), stating that every {Full-size image (25 K),Full-size image (25 K)}-graph is a SEG-graph, we investigate several known subclasses of SEG-graphs and show that they are {Full-size image (25 K)}-graphs, or Bk-VPG-graphs for some small constant k. We show that all planar 3-trees, all line graphs of planar graphs, and all full subdivisions of planar graphs are {Full-size image (25 K)}-graphs. Furthermore we show that complements of planar graphs are B17-VPG-graphs and complements of full subdivisions are B2-VPG-graphs. Here a full subdivision is a graph in which each edge is subdivided at least once.

Item Type:Article
Full text:(AM) Accepted Manuscript
Available under License - Creative Commons Attribution Non-commercial No Derivatives.
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Publisher statement:© 2016 This manuscript version is made available under the CC-BY-NC-ND 4.0 license
Date accepted:22 January 2016
Date deposited:15 February 2016
Date of first online publication:19 February 2016
Date first made open access:19 February 2017

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