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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 & Algorithms, 48 (2). pp. 270-289. ISSN 1042-9832

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Identification Number: 10.1002/rsa.20593


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
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Additional Information: © 2015 Wiley Periodicals, Inc.
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 26 Jan 2016 14:15
Last Modified: 20 Aug 2021 02:06

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