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Spanning embeddings of arrangeable graphs with sublinear bandwidth
2015
Random structures & algorithms (Print)
The Bandwidth Theorem of Böttcher, Schacht, and Taraz [Mathematische Annalen 343 (1), 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 ( 3 4 + γ)n contain almost all planar graphs on n vertices as subgraphs. Using
doi:10.1002/rsa.20593
fatcat:doc423tz7neqfjbiorduj44uey