Spanning embeddings of arrangeable graphs with sublinear bandwidth |
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Authors: | Julia Böttcher Anusch Taraz Andreas Würfl |
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Institution: | 1. Department of Mathematics, London School of Economics, London, UK;2. Institut für Mathematik, Technische Universit?t Hamburg, Hamburg, Germany;3. Zentrum Mathematik, Technische Universit?t München, Garching bei München, Germany |
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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 , where n is the number of vertices of H. Our result implies that sufficiently large n‐vertex graphs G with minimum degree at least 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 . We obtain corresponding results for graphs embeddable on different orientable surfaces. © 2015 Wiley Periodicals, Inc. Random Struct. Alg., 48, 270–289, 2016 |
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Keywords: | graph embedding bandwidth theorem arrangeable graphs Ramsey numbersregularity method |
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