Böttcher, Julia, Schacht , Mathais and Taraz, Anusch
(2007)
*On the bandwidth conjecture for 3-colourable graphs.*
In:
Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms.
Society for Industrial and Applied Mathematics, pp. 618-626.
ISBN 9780898716245

## Abstract

A conjecture by Bollob´as and Koml´os states that for every γ > 0 and integers r ≥ 2 andΔ, there exists β > 0 such that for sufficiently large n the following holds: If G is a graph on n vertices with minimum degree at least ((r−1)/r +γ)n and H is an r-chromatic graph on n vertices with bandwidth at most βn and maximum degree at most Δ, then G contains a copy of H. This conjecture generalises several results concerning sufficient degree conditions for the containment of spanning subgraphs. We prove the conjecture for the case r = 3. Our proof yields a polynomial time algorithm for embedding H into G if H is given together with a 3-colouring and vertex labelling respecting the bandwidth bound.

Item Type: | Book Section |
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Additional Information: | © 2007 Society for Industrial and Applied Mathematics |

Library of Congress subject classification: | Q Science > QA Mathematics |

Sets: | Departments > Mathematics |

Rights: | http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx |

Date Deposited: | 28 May 2012 15:49 |

URL: | http://eprints.lse.ac.uk/44115/ |

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