Spanning embeddings of arrangeable graphs with sublinear bandwidth
نویسندگان
چکیده
The Bandwidth Theorem of Böttcher, Schacht and Taraz [Mathematische Annalen 343 (1), 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 ∆(H) ≤ √ n/ log n, where n is the number of vertices of H. Our result implies that sufficiently large n-vertex graphs G with minimum degree at least ( 4 + γ)n contain almost all planar graphs on n vertices as subgraphs. Using techniques developed by Allen, Brightwell and Skokan [Combinatorica, to appear] we can also apply our methods to show that almost all planar graphs H have Ramsey number at most 12|H|. We obtain corresponding results for graphs embeddable on different orientable surfaces.
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عنوان ژورنال:
- Random Struct. Algorithms
دوره 48 شماره
صفحات -
تاریخ انتشار 2016