Embedding degenerate graphs of small bandwidth

Abstract

We develop a tool for embedding almost spanning degenerate graphs of small bandwidth. As an application, we extend the blow-up lemma to degenerate graphs of small bandwidth, the bandwidth theorem to degenerate graphs, and make progress on a conjecture of Burr and Erdős on Ramsey number of degenerate graphs.

39 pages, 2 figures

References in corpus (3)

• The Ramsey number of the clique and the hypercube
• Spanning embeddings of arrangeable graphs with sublinear bandwidth
• An Extension of the Blow-up Lemma to arrangeable graphs

Cited by in corpus (2)

• The bandwidth theorem for locally dense graphs
• A transference principle for Ramsey numbers of bounded degree graphs