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Representing a cubic graph as the intersection graph of axis-parallel boxes in three dimensions

Adiga, Abhijin and Chandran, Sunil L (2012) Representing a cubic graph as the intersection graph of axis-parallel boxes in three dimensions. In: 12 Proceedings of the 2012 symposuim on Computational Geometry, June 17-20, 2012, Chapel Hill, NC, USA.

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Official URL: http://dx.doi.org/10.1145/2261250.2261309

Abstract

We show that every graph of maximum degree 3 can be represented as the intersection graph of axis parallel boxes in three dimensions, that is, every vertex can be mapped to an axis parallel box such that two boxes intersect if and only if their corresponding vertices are adjacent. In fact, we construct a representation in which any two intersecting boxes just touch at their boundaries. Further, this construction can be realized in linear time.

Item Type: Conference Paper
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Additional Information: Copyright of this article belongs to ACM Press.
Keywords: Cubic Graphs; Intersection Graphs; Axis Parallel Boxes; Boxi- City
Department/Centre: Division of Electrical Sciences > Computer Science & Automation (Formerly, School of Automation)
Date Deposited: 02 Jul 2013 08:37
Last Modified: 02 Jul 2013 08:37
URI: http://eprints.iisc.ernet.in/id/eprint/46679

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