Library Header Image
LSE Research Online LSE Library Services

On the bandwidth conjecture for 3-colourable graphs

Böttcher, Julia ORCID: 0000-0002-4104-3635, 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

Full text not available from this repository.


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
Additional Information: © 2007 Society for Industrial and Applied Mathematics
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 28 May 2012 15:49
Last Modified: 16 May 2024 05:10

Actions (login required)

View Item View Item