ePrints@IIScePrints@IISc Home | About | Browse | Latest Additions | Advanced Search | Contact | Help

The cubicity of hypercube graphs

Chandran, Sunil L and Sivadasan, Naveen (2008) The cubicity of hypercube graphs. In: Discrete Mathematics, 308 (23). pp. 5795-5800.

[img] PDF
full.pdf - Published Version
Restricted to Registered users only

Download (246kB) | Request a copy
Official URL: http://www.sciencedirect.com/science?_ob=ArticleUR...


For a graph G, its cubicity View the MathML source is the minimum dimension k such that Gis representable as the intersection graph of (axis-parallel) cubes in k-dimensional space. (A k-dimensional cube is a Cartesian product R1×R2×cdots, three dots, centered×Rk, where Ri is a closed interval of the form [ai,ai+1] on the real line.) Chandran et al. [L.S. Chandran, C. Mannino, G. Oriolo, On the cubicity of certain graphs, Information Processing Letters 94 (2005) 113–118] showed that for a d-dimensional hypercube Hd, View the MathML source. In this paper, we use the probabilistic method to show that View the MathML source. The parameter boxicity generalizes cubicity: the boxicity View the MathML source of a graph G is defined as the minimum dimension k such that G is representable as the intersection graph of axis-parallel boxes in k-dimensional space. Since View the MathML source for any graph G, our result implies that View the MathML source. The problem of determining a non-trivial lower bound for View the MathML source is left open.

Item Type: Journal Article
Publication: Discrete Mathematics
Publisher: Elsevier Science
Additional Information: Copyright of this article belongs to Elsevier Science.
Keywords: Cubicity;Boxicity;Hypercube.
Department/Centre: Division of Electrical Sciences > Computer Science & Automation
Date Deposited: 21 Aug 2009 08:29
Last Modified: 28 Feb 2019 08:40
URI: http://eprints.iisc.ac.in/id/eprint/17549

Actions (login required)

View Item View Item