Bhowmick, Diptendu and Chandran, Sunil L
(2010)
*Boxicity and cubicity of asteroidal triple free graphs.*
In: Discrete Mathematics, 310
(10-11).
pp. 1536-1543.

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## Abstract

The boxicity of a graph G, denoted box(G), is the least integer d such that G is the intersection graph of a family of d-dimensional (axis-parallel) boxes. The cubicity, denoted cub(G), is the least dsuch that G is the intersection graph of a family of d-dimensional unit cubes. An independent set of three vertices is an asteroidal triple if any two are joined by a path avoiding the neighbourhood of the third. A graph is asteroidal triple free (AT-free) if it has no asteroidal triple. The claw number psi(G) is the number of edges in the largest star that is an induced subgraph of G. For an AT-free graph G with chromatic number chi(G) and claw number psi(G), we show that box(G) <= chi(C) and that this bound is sharp. We also show that cub(G) <= box(G)([log(2) psi(G)] + 2) <= chi(G)([log(2) psi(G)] + 2). If G is an AT-free graph having girth at least 5, then box(G) <= 2, and therefore cub(G) <= 2 [log(2) psi(G)] + 4. (c) 2010 Elsevier B.V. All rights reserved.

Item Type: | Journal Article |
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Publication: | Discrete Mathematics |

Publisher: | Elsevier Science |

Additional Information: | Copyright of this article belongs to Elsevier Science. |

Keywords: | Boxicity; Cubicity; Chordal dimension; Asteroidal triple free graph; Chromatic number; Claw number |

Department/Centre: | Division of Electrical Sciences > Computer Science & Automation |

Date Deposited: | 04 Jun 2010 04:33 |

Last Modified: | 19 Sep 2010 06:06 |

URI: | http://eprints.iisc.ac.in/id/eprint/27719 |

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