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Spanning embeddings of arrangeable graphs with sublinear bandwidth

Böttcher, Julia, 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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Identification Number: 10.1002/rsa.20593

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
Sets: Departments > Mathematics
Date Deposited: 26 Jan 2016 14:15
Last Modified: 20 Mar 2019 02:46
URI: http://eprints.lse.ac.uk/id/eprint/65152

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