Boxicity of Line Graphs

Chandran, Sunil L and Mathew, Rogers and Sivadasan, Naveen (2010) Boxicity of Line Graphs. UNSPECIFIED.

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Abstract

The boxicity of a graph H, denoted by View the MathML source, is the minimum integer k such that H is an intersection graph of axis-parallel k-dimensional boxes in View the MathML source. In this paper we show that for a line graph G of a multigraph, View the MathML source, where Δ(G) denotes the maximum degree of G. Since G is a line graph, Δ(G)≤2(χ(G)−1), where χ(G) denotes the chromatic number of G, and therefore, View the MathML source. For the d-dimensional hypercube Qd, we prove that View the MathML source. The question of finding a nontrivial lower bound for View the MathML source 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).

Item Type:	Departmental Technical Report
Keywords:	Intersection graph;Interval graph;Boxicity;Line graph;Edge graph;Hypercube;Subdivision.
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	09 Nov 2011 06:41
Last Modified:	09 Nov 2011 06:41
URI:	http://eprints.iisc.ac.in/id/eprint/40343

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