Publisher DOI: 10.1137/13093827X
Title: An extension of the blow-up lemma to arrangeable graphs
Language: English
Authors: Böttcher, Julia 
Kohayakawa, Yoshiharu 
Taraz, Anusch 
Würfl, Andreas 
Keywords: Arrangeable graphs; Blow-up lemma; Graph embeddings; Regularity lemma; Spanning subgraphs
Issue Date: 4-Jun-2015
Publisher: Soc.
Source: SIAM Journal on Discrete Mathematics 29 (2): 962-1001 (2015)
Abstract (english): 
The blow-up lemma established by Komlós, Sárközy, and Szemerédi in 1997 is an important tool for the embedding of spanning subgraphs of bounded maximum degree. Here we prove several generalizations of this result concerning the embedding of a-arrangeable graphs, where a graph is called a-arrangeable if its vertices can be ordered in such a way that the neighbors to the right of any vertex v have at most a neighbors to the left of v in total. Examples of arrangeable graphs include planar graphs and, more generally, graphs without a Ks-subdivision for constant s. Our main result shows that a-arrangeable graphs with maximum degree at most √ n/ log n can be embedded into corresponding systems of superregular pairs. This is optimal up to the logarithmic factor. We also present two applications. We prove that any large enough graph G with minimum degree at least (r-1 r + γ)n contains an F-factor of every a-arrangeable r-chromatic graph F with at most ζn vertices and maximum degree at most √ n/ log n, as long as ζ is sufficiently small compared to γ/(ar). This extends a result of Alon and Yuster [J. Combin. Theory Ser. B, 66 (1996), pp. 269-282]. Moreover, we show that for constant p the random graph G(n, p) is universal for the class of a-arrangeable n-vertex graphs H of maximum degree at most ζn/ log n, as long as ζ is sufficiently small compared to p/a. © 2015 Society for Industrial and Applied Mathematics.
ISSN: 1095-7146
Journal: SIAM journal on discrete mathematics 
Institute: Mathematik E-10 
Document Type: Article
Appears in Collections:Publications without fulltext

Show full item record

Page view(s)

Last Week
Last month
checked on Jul 5, 2022


Last Week
Last month
checked on Jun 30, 2022

Google ScholarTM


Add Files to Item

Note about this record

Cite this record


Items in TORE are protected by copyright, with all rights reserved, unless otherwise indicated.