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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 (2014) REPRESENTING A CUBIC GRAPH AS THE INTERSECTION GRAPH OF AXIS-PARALLEL BOXES IN THREE DIMENSIONS. In: SIAM JOURNAL ON DISCRETE MATHEMATICS, 28 (3). pp. 1515-1539.

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Official URL: http://dx.doi.org/ 10.1137/120861795

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 touch just at their boundaries.

Item Type: Journal Article
Additional Information: Copy right for this article belongs to the SIAM PUBLICATIONS, 3600 UNIV CITY SCIENCE CENTER, PHILADELPHIA, PA 19104-2688 USA
Keywords: cubic graphs; intersection graphs; axis parallel boxes; boxicity
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Depositing User: Id for Latest eprints
Date Deposited: 20 Nov 2014 04:18
Last Modified: 20 Nov 2014 04:18
URI: http://eprints.iisc.ac.in/id/eprint/50298

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