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 |
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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 |

Depositing User: | Id for Latest eprints |

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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