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Asymptotic multipartite version of the Alon–Yuster theorem

Martin, Ryan R. and Skokan, Jozef ORCID: 0000-0003-3996-7676 (2017) Asymptotic multipartite version of the Alon–Yuster theorem. Journal of Combinatorial Theory, Series B, 127. pp. 32-52. ISSN 0095-8956

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Identification Number: 10.1016/j.jctb.2017.05.004

Abstract

In this paper, we prove the asymptotic multipartite version of the Alon–Yuster theorem, which is a generalization of the Hajnal–Szemerédi theorem: If k≥3 is an integer, H is a k -colorable graph and γ>0 is fixed, then, for every sufficiently large n , where |V(H)| divides n, and for every balanced k-partite graph G on kn vertices with each of its corresponding View the MathML source bipartite subgraphs having minimum degree at least (k−1)n/k+γn, G has a subgraph consisting of kn/|V(H)| vertex-disjoint copies of H. The proof uses the Regularity method together with linear programming.

Item Type: Article
Official URL: https://www.journals.elsevier.com/journal-of-combi...
Additional Information: © 2017 Elsevier Inc.
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 05 Jun 2017 09:31
Last Modified: 20 Oct 2021 02:31
URI: http://eprints.lse.ac.uk/id/eprint/79884

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