Separation Dimension of Graphs and Hypergraphs

Manu Basavaraju; L. Sunil Chandran; Martin Charles Golumbic; Rogers Mathew; Deepak Rajendraprasad

doi:10.1007/s00453-015-0050-6

Separation Dimension of Graphs and Hypergraphs

Manu Basavaraju, L. Sunil Chandran, Martin Charles Golumbic, Rogers Mathew, Deepak Rajendraprasad

Department of Computer Science

Research output: Contribution to journal › Article › peer-review

Abstract

Separation dimension of a hypergraph H, denoted by π( H) , is the smallest natural number k so that the vertices of H can be embedded in R^k such that any two disjoint edges of H can be separated by a hyperplane normal to one of the axes. We show that the separation dimension of a hypergraph H is equal to the boxicity of the line graph of H. This connection helps us in borrowing results and techniques from the extensive literature on boxicity to study the concept of separation dimension. In this paper, we study the separation dimension of hypergraphs and graphs.

Original language	English
Pages (from-to)	187-204
Number of pages	18
Journal	Algorithmica
Volume	75
Issue number	1
DOIs	https://doi.org/10.1007/s00453-015-0050-6
State	Published - 1 May 2016

Bibliographical note

Publisher Copyright:
© 2015, Springer Science+Business Media New York.

Keywords

Acyclic chromatic number
Boxicity
Line graph
Scrambling permutation
Separation dimension

ASJC Scopus subject areas

General Computer Science
Computer Science Applications
Applied Mathematics

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10.1007/s00453-015-0050-6

Cite this

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AU - Chandran, L. Sunil

AU - Golumbic, Martin Charles

AU - Mathew, Rogers

AU - Rajendraprasad, Deepak

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AB - Separation dimension of a hypergraph H, denoted by π( H) , is the smallest natural number k so that the vertices of H can be embedded in Rk such that any two disjoint edges of H can be separated by a hyperplane normal to one of the axes. We show that the separation dimension of a hypergraph H is equal to the boxicity of the line graph of H. This connection helps us in borrowing results and techniques from the extensive literature on boxicity to study the concept of separation dimension. In this paper, we study the separation dimension of hypergraphs and graphs.

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JO - Algorithmica

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Separation Dimension of Graphs and Hypergraphs

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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