Completing partial packings of bipartite graphs

Zoltán Füredi; Ago Erik Riet; Mykhaylo Tyomkyn

doi:10.1016/j.jcta.2011.06.009

Completing partial packings of bipartite graphs

Zoltán Füredi, Ago Erik Riet, Mykhaylo Tyomkyn^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

Given a bipartite graph H and an integer n, let f(n;H) be the smallest integer such that any set of edge disjoint copies of H on n vertices can be extended to an H-design on at most n+f(n;H) vertices. We establish tight bounds for the growth of f(n;H) as n→∞. In particular, we prove the conjecture of Füredi and Lehel (2010) [4] that f(n;H)=o(n). This settles a long-standing open problem.

Original language	English
Pages (from-to)	2463-2473
Number of pages	11
Journal	Journal of Combinatorial Theory - Series A
Volume	118
Issue number	8
DOIs	https://doi.org/10.1016/j.jcta.2011.06.009
State	Published - Nov 2011
Externally published	Yes

Keywords

Designs
Graph embeddings
Graph packings

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10.1016/j.jcta.2011.06.009

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title = "Completing partial packings of bipartite graphs",

abstract = "Given a bipartite graph H and an integer n, let f(n;H) be the smallest integer such that any set of edge disjoint copies of H on n vertices can be extended to an H-design on at most n+f(n;H) vertices. We establish tight bounds for the growth of f(n;H) as n→∞. In particular, we prove the conjecture of F{\"u}redi and Lehel (2010) [4] that f(n;H)=o(n). This settles a long-standing open problem.",

keywords = "Designs, Graph embeddings, Graph packings",

author = "Zolt{\'a}n F{\"u}redi and Riet, {Ago Erik} and Mykhaylo Tyomkyn",

note = "Funding Information: OTKA, and by the National Science Foundation Funding Information: E-mail address: m.tyomkyn@dpmms.cam.ac.uk (M. Tyomkyn). 1 Research supported in part by the Hungarian National Science Foundation under grant NFS DMS 09-01276 ARRA.",

year = "2011",

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doi = "10.1016/j.jcta.2011.06.009",

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AU - Riet, Ago Erik

AU - Tyomkyn, Mykhaylo

N1 - Funding Information: OTKA, and by the National Science Foundation Funding Information: E-mail address: m.tyomkyn@dpmms.cam.ac.uk (M. Tyomkyn). 1 Research supported in part by the Hungarian National Science Foundation under grant NFS DMS 09-01276 ARRA.

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N2 - Given a bipartite graph H and an integer n, let f(n;H) be the smallest integer such that any set of edge disjoint copies of H on n vertices can be extended to an H-design on at most n+f(n;H) vertices. We establish tight bounds for the growth of f(n;H) as n→∞. In particular, we prove the conjecture of Füredi and Lehel (2010) [4] that f(n;H)=o(n). This settles a long-standing open problem.

AB - Given a bipartite graph H and an integer n, let f(n;H) be the smallest integer such that any set of edge disjoint copies of H on n vertices can be extended to an H-design on at most n+f(n;H) vertices. We establish tight bounds for the growth of f(n;H) as n→∞. In particular, we prove the conjecture of Füredi and Lehel (2010) [4] that f(n;H)=o(n). This settles a long-standing open problem.

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KW - Graph packings

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JO - Journal of Combinatorial Theory - Series A

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IS - 8

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Completing partial packings of bipartite graphs

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