Product Dimension of Forests and Bounded Treewidth Graphs

Chandran, Sunil L and Mathew, Rogers and Rajendraprasad, Deepak and Sharma, Roohani (2013) Product Dimension of Forests and Bounded Treewidth Graphs. In: ELECTRONIC JOURNAL OF COMBINATORICS, 20 (3).

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Abstract

The product dimension of a graph G is defined as the minimum natural number l such that G is an induced subgraph of a direct product of l complete graphs. In this paper we study the product dimension of forests, bounded treewidth graphs and k-degenerate graphs. We show that every forest on n vertices has product dimension at most 1.441 log n + 3. This improves the best known upper bound of 3 log n for the same due to Poljak and Pultr. The technique used in arriving at the above bound is extended and combined with a well-known result on the existence of orthogonal Latin squares to show that every graph on n vertices with treewidth at most t has product dimension at most (t + 2) (log n + 1). We also show that every k-degenerate graph on n vertices has product dimension at most inverted right perpendicular5.545 k log ninverted left perpendicular + 1. This improves the upper bound of 32 k log n for the same by Eaton and Rodl.

Item Type:	Journal Article
Publication:	ELECTRONIC JOURNAL OF COMBINATORICS
Publisher:	ELECTRONIC JOURNAL OF COMBINATORICS
Additional Information:	Copyright of this article is belongs to ELECTRONIC JOURNAL OF COMBINATORICS
Keywords:	product dimension; representation number; forest; bounded treewidth graph; k-degenerate graph; orthogonal Latin squares
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	25 Oct 2013 14:58
Last Modified:	25 Oct 2013 14:58
URI:	http://eprints.iisc.ac.in/id/eprint/47576

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