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An improved error term for minimum H-decompositions of graphs

Allen, Peter, Böttcher, Julia and Person, Yury (2014) An improved error term for minimum H-decompositions of graphs. Journal of Combinatorial Theory, Series B, Online . ISSN 0095-8956 (In Press)

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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.
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Date Deposited: 08 May 2014 13:10
URL: http://eprints.lse.ac.uk/56670/

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