Library Header Image
LSE Research Online LSE Library Services

The bandwidth theorem in sparse graphs

Allen, Peter, Böttcher, Julia, Ehrenmüller, Julia and Taraz, Anusch (2020) The bandwidth theorem in sparse graphs. Advances in Combinatorics, 2020 (1). 1 - 60. ISSN 2517-5599

[img] Text (The bandwidth theorem in sparse graphs) - Published Version
Available under License Creative Commons Attribution.

Download (820kB)

Identification Number: 10.19086/aic.12849


The bandwidth theorem [Mathematische Annalen, 343(1):175–205, 2009] states that any n-vertex graph G with minimum degree [Formula Presented] contains all n-vertex k-colourable graphs H with bounded maximum degree and bandwidth o(n). We provide sparse analogues of this statement in random graphs as well as pseudorandom graphs. More precisely, we show that for p ≫[Formula Presented] asymptotically almost surely each spanning subgraph G of G(n, p) with minimum degree [Formula Presented] pn contains all n-vertex k-colourable graphs H with maximum degree ∆, bandwidth o(n), and at least Cp−2 vertices not contained in any triangle. A similar result is shown for sufficiently bijumbled graphs, which, to the best of our knowledge, is the first resilience result in pseudorandom graphs for a rich class of spanning subgraphs. Finally, we provide improved results for H with small degeneracy, which in particular imply a resilience result in G(n, p) with respect to the containment of spanning bounded degree trees for p ≫[Formula Presented].

Item Type: Article
Official URL:
Additional Information: © 2020 The Authors
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 24 Sep 2020 12:51
Last Modified: 20 Jul 2021 02:59

Actions (login required)

View Item View Item


Downloads per month over past year

View more statistics