Böttcher, Julia and Müller, Sybille
(2009)
*Forcing spanning subgraphs via Ore type conditions.*
Electronic Notes in Discrete Mathematics, 34.
pp. 255-259.
ISSN 1571-0653

## Abstract

We determine an Ore type condition that allows the embedding of 3-colourable bounded degree graphs of sublinear bandwidth: For all Δ,γ>0 there are β,n0>0 such that for all n⩾n0 the following holds. Let G=(V,E) and H be n-vertex graphs such that H is 3-colourable, has maximum degree Δ(H)⩽Δ and bandwidth bw(H)⩽βn, and G satisfies deg(u)+deg(v)⩾(4/3+γ)n for all uv∉E. Then G contains a copy of H. This improves on the Bollobás-Komlós conjecture for 3-chromatic graphs proven by Böttcher, Schacht, and Taraz [J. Combin. Theory, Ser. B, 98(4), 752–777, 2008] and applies a result of Kierstaed and Kostochka [J. Comb. Theory, Ser. B, 98(1), 226–234, 2008] about the existence of spanning triangle factors under Ore type conditions.

Item Type: | Article |
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Official URL: | http://www.elsevier.com/wps/find/journaldescriptio... |

Additional Information: | © 2009 Elsevier B.V. |

Subjects: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Date Deposited: | 28 May 2012 15:30 |

Last Modified: | 28 May 2012 15:30 |

URI: | http://eprints.lse.ac.uk/id/eprint/44109 |

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