Allen, Peter 
ORCID: 0000-0001-6555-3501, Böttcher, Julia ORCID: 0000-0002-4104-3635 and Person, Yury
(2014)
An improved error term for minimum H-decompositions of graphs.
Journal of Combinatorial Theory, Series B, 108.
pp. 92-101.
ISSN 0095-8956
Abstract
We consider partitions of the edge set of a graph G into copies of a fixed graph H and single edges. Let ϕH(n) denote the minimum number p such that any n-vertex G admits such a partition with at most p parts. We show that ϕH(n)=ex(n,Kr)+Θ(biex(n,H)) for χ(H)=r≥3, where biex(n,H) is the extremal number of the decomposition family of H. Since biex(n,H)=O(n2−γ) for some γ>0 this improves on the bound ϕH(n)=ex(n,H)+o(n2) by Pikhurko and Sousa (2007). In addition, it extends a result of Özkahya and Person (2012).
| Item Type: | Article |
|---|---|
| Official URL: | http://www.journals.elsevier.com/journal-of-combin... |
| Additional Information: | © 2014 Elsevier Inc. |
| Divisions: | Mathematics |
| Subjects: | Q Science > QA Mathematics |
| Date Deposited: | 08 May 2014 13:10 |
| Last Modified: | 01 Oct 2024 03:41 |
| Projects: | Proc. 2010/09555-7, 2009/17831-7, I-889-182.6/2005, 415/ppp-probral/po/D08/11629, Proj. No. 333/09 |
| Funders: | Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), Graphics Interchange Format (GIF), CAPES–DAAD project, CAPES–DAAD project |
| URI: | http://eprints.lse.ac.uk/id/eprint/56670 |
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