Blow-up lemmas for sparse graphs

Allen, Peter ORCID: 0000-0001-6555-3501, Böttcher, Julia ORCID: 0000-0002-4104-3635, Hàn, Hiệp, Kohayakawa, Yoshiharu and Person, Yury (2025) Blow-up lemmas for sparse graphs. Discrete Analysis, 2025 (8). ISSN 2397-3129

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Abstract

The blow-up lemma states that a system of super-regular pairs contains all bounded degree spanning graphs as subgraphs that embed into a corresponding system of complete pairs. This lemma has far-reaching applications in extremal combinatorics. We prove sparse analogues of the blow-up lemma for subgraphs of random and of pseudorandom graphs. Our main results are the following three sparse versions of the blow-up lemma: one for embedding spanning graphs with maximum degree ∆ in subgraphs of G(n, p) with p = C(logn/n) 1/∆ ; one for embedding spanning graphs with maximum degree ∆ and degeneracy D in subgraphs of G(n, p) with p = C (logn/n) 1/(2D+1) ; and one for embedding spanning graphs with maximum degree ∆ in (p, cpmax(4,(3∆+1)/2)n)-bijumbled graphs. We also consider various applications of these lemmas

Item Type:	Article
Additional Information:	© 2025 The Authors
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	07 Feb 2024 11:45
Last Modified:	01 Oct 2025 04:36
URI:	http://eprints.lse.ac.uk/id/eprint/121964

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