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