Projects per year
The Bandwidth theorem of B¨ottcher, Schacht and Taraz [Proof of the bandwidth conjecture of Bollob´as and Koml´os, Mathematische Annalen, 2009] gives a condition on the minimum degree of an n-vertex graph G that ensures G contains every r-chromatic graph H on n vertices of bounded degree and of bandwidth o(n), thereby proving a conjecture of Bollob´as and Koml´os [The Blow-up Lemma, Combinatorics, Probability and Computing, 1999]. In this paper we prove a version of the Bandwidth theorem for locally dense graphs. Indeed, we prove that every locally dense n-vertex graph G with δ(G) > (1/2 + o(1))n contains as a subgraph any given (spanning) H with bounded maximum degree and sublinear bandwidth.
|Number of pages||36|
|Journal||Forum of Mathematics, Sigma|
|Publication status||Published - 4 Nov 2020|
- regularity method
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- 1 Finished
EPSRC Fellowship: Dr Andrew Treglown - Independence in groups, graphs and the integers
Engineering & Physical Science Research Council
1/06/15 → 31/05/18
Project: Research Councils