Boxicity of line graphs

Chandran, Sunil L and Mathew, Rogers and Sivadasan, Naveen (2011) Boxicity of line graphs. In: Discrete Mathematics, 311 (21). pp. 2359-2367.

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Abstract

The boxicity of a graph H, denoted by box(H), is the minimum integer k such that H is an intersection graph of axis-parallel k-dimensional boxes in R(k). In this paper we show that for a line graph G of a multigraph, box(G) <= 2 Delta (G)(inverted right perpendicularlog(2) log(2) Delta(G)inverted left perpendicular + 3) + 1, where Delta(G) denotes the maximum degree of G. Since G is a line graph, Delta(G) <= 2(chi (G) - 1), where chi (G) denotes the chromatic number of G, and therefore, box(G) = 0(chi (G) log(2) log(2) (chi (G))). For the d-dimensional hypercube Q(d), we prove that box(Q(d)) >= 1/2 (inverted right perpendicularlog(2) log(2) dinverted left perpendicular + 1). The question of finding a nontrivial lower bound for box(Q(d)) was left open by Chandran and Sivadasan in [L. Sunil Chandran, Naveen Sivadasan, The cubicity of Hypercube Graphs. Discrete Mathematics 308 (23) (2008) 5795-5800]. The above results are consequences of bounds that we obtain for the boxicity of a fully subdivided graph (a graph that can be obtained by subdividing every edge of a graph exactly once). (C) 2011 Elsevier B.V. All rights reserved.

Item Type:	Editorials/Short Communications
Publication:	Discrete Mathematics
Publisher:	Elseveir Science
Additional Information:	Copyright of this article belongs to Elseveir Science.
Keywords:	Intersection graph;Interval graph;Boxicity;Line graph;Edge graph;Hypercube;Subdivision
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	03 Nov 2011 08:41
Last Modified:	03 Nov 2011 08:41
URI:	http://eprints.iisc.ac.in/id/eprint/41814

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