SEPARATION DIMENSION OF BOUNDED DEGREE GRAPHS

Alon, Noga and Basavaraju, Manu and Chandran, Sunil L and Mathew, Rogers and Rajendraprasad, Deepak (2015) SEPARATION DIMENSION OF BOUNDED DEGREE GRAPHS. In: SIAM JOURNAL ON DISCRETE MATHEMATICS, 29 (1). pp. 59-64.

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Abstract

The separation dimension of a graph G is the smallest natural number k for which the vertices of G can be embedded in R-k such that any pair of disjoint edges in G can be separated by a hyperplane normal to one of the axes. Equivalently, it is the smallest possible cardinality of a family F of total orders of the vertices of G such that for any two disjoint edges of G, there exists at least one total order in F in which all the vertices in one edge precede those in the other. In general, the maximum separation dimension of a graph on n vertices is Theta(log n). In this article, we focus on bounded degree graphs and show that the separation dimension of a graph with maximum degree d is at most 2(9) (log*d)d. We also demonstrate that the above bound is nearly tight by showing that, for every d, almost all d-regular graphs have separation dimension at least d/2]

Item Type:	Journal Article
Publication:	SIAM JOURNAL ON DISCRETE MATHEMATICS
Publisher:	SIAM PUBLICATIONS
Additional Information:	Copy right for this article belongs to the SIAM PUBLICATIONS, 3600 UNIV CITY SCIENCE CENTER, PHILADELPHIA, PA 19104-2688 USA
Keywords:	separation dimension; boxicity; linegraph; bounded degree
Department/Centre:	Division of Electrical Sciences > Computer Science & Automation
Date Deposited:	06 May 2015 05:40
Last Modified:	06 May 2015 05:40
URI:	http://eprints.iisc.ac.in/id/eprint/51504

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