Spanning embeddings of arrangeable graphs with sublinear bandwidth

Böttcher, Julia ORCID: 0000-0002-4104-3635, Taraz, Anusch and Würfl, Andreas (2015) Spanning embeddings of arrangeable graphs with sublinear bandwidth. Random Structures and Algorithms, 48 (2). pp. 270-289. ISSN 1042-9832

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Abstract

The Bandwidth Theorem of Böttcher, et al. [Mathematische Annalen 343 (2009), 175–205] gives minimum degree conditions for the containment of spanning graphs H with small bandwidth and bounded maximum degree. We generalise this result to a-arrangeable graphs H with inline image, where n is the number of vertices of H. Our result implies that sufficiently large n-vertex graphs G with minimum degree at least inline image contain almost all planar graphs on n vertices as subgraphs. Using techniques developed by Allen, et al. [Combinatorica 33 (2013), 125–160] we can also apply our methods to show that almost all planar graphs H have Ramsey number at most inline image. We obtain corresponding results for graphs embeddable on different orientable surfaces

Item Type:	Article
Official URL:	http://onlinelibrary.wiley.com/journal/10.1002/(IS...
Additional Information:	© 2015 Wiley Periodicals, Inc.
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	26 Jan 2016 14:15
Last Modified:	12 Dec 2024 00:59
URI:	http://eprints.lse.ac.uk/id/eprint/65152

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