An asymptotic multipartite Kühn-Osthus theorem

Ryan Martin; Richard Mycroft; Jozef Skokan

doi:10.1137/16M1070621

An asymptotic multipartite Kühn-Osthus theorem

Ryan Martin, Richard Mycroft, Jozef Skokan

Mathematics

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Abstract

In this paper we prove an asymptotic multipartite version of a well-known theorem of K"uhn and Osthus by establishing, for any graph H with chromatic number r, the asymptotic multipartite minimum degree threshold which ensures that a large r-partite graph G admits a perfect H-tiling. We also give the threshold for an H-tiling covering all but a linear number of vertices of G, in a multipartite analogue of results of Koml\'os and of Shokoufandeh and Zhao.

Original language	English
Pages (from-to)	1498-1513
Number of pages	16
Journal	SIAM Journal on Discrete Mathematics
Volume	31
Issue number	3
DOIs	https://doi.org/10.1137/16M1070621
Publication status	Published - 13 Jul 2017

Keywords

tiling
Hajnal-Szemer´edi
K¨uhn-Osthus
multipartite
regularity
linear programming

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10.1137/16M1070621Licence: None: All rights reserved

Martin_et_al_An_asymptotic_multipartite_SIAM_Journal_on_Discrete_Mathematics_2017
© 2017, Society for Industrial and Applied Mathematics
Final published version, 377 KBLicence: Other (please specify with Rights Statement)

http://epubs.siam.org/doi/10.1137/16M1070621Licence: None: All rights reserved

Embeddings in hypergraphs
Mycroft, R.
Engineering & Physical Science Research Council
30/03/15 → 29/03/17
Project: Research Councils

Cite this

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AU - Skokan, Jozef

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N2 - In this paper we prove an asymptotic multipartite version of a well-known theorem of K"uhn and Osthus by establishing, for any graph H with chromatic number r, the asymptotic multipartite minimum degree threshold which ensures that a large r-partite graph G admits a perfect H-tiling. We also give the threshold for an H-tiling covering all but a linear number of vertices of G, in a multipartite analogue of results of Koml\'os and of Shokoufandeh and Zhao.

AB - In this paper we prove an asymptotic multipartite version of a well-known theorem of K"uhn and Osthus by establishing, for any graph H with chromatic number r, the asymptotic multipartite minimum degree threshold which ensures that a large r-partite graph G admits a perfect H-tiling. We also give the threshold for an H-tiling covering all but a linear number of vertices of G, in a multipartite analogue of results of Koml\'os and of Shokoufandeh and Zhao.

KW - tiling

KW - Hajnal-Szemer´edi

KW - K¨uhn-Osthus

KW - multipartite

KW - regularity

KW - linear programming

U2 - 10.1137/16M1070621

DO - 10.1137/16M1070621

M3 - Article

SN - 0895-4801

VL - 31

SP - 1498

EP - 1513

JO - SIAM Journal on Discrete Mathematics

JF - SIAM Journal on Discrete Mathematics

IS - 3

ER -

An asymptotic multipartite Kühn-Osthus theorem

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