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Decomposing graphs into edges and triangles

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Králʼ, Daniel, Lidicky, Bernard, Martins, Taisa and Pehova, Yanitsa (2019) Decomposing graphs into edges and triangles. Combinatorics, Probability and Computing, 28 (3). pp. 465-472. doi:10.1017/S0963548318000421 ISSN 0963-5483.

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Official URL: https://doi.org/10.1017/S0963548318000421

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Abstract

We prove the following 30 year-old conjecture of Győri and Tuza: the edges of every n-vertex graph G can be decomposed into complete graphs C1,. . .,Cℓ of orders two and three such that |C1|+···+|Cℓ| ≤ (1/2+o(1))n2. This result implies the asymptotic version of the old result of Erdős, Goodman and Pósa that asserts the existence of such a decomposition with ℓ ≤ n2/4.

Item Type: Journal Article
Divisions: Faculty of Science, Engineering and Medicine > Science > Computer Science
Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title: Combinatorics, Probability and Computing
Publisher: Cambridge University Press
ISSN: 0963-5483
Official Date: May 2019
Dates:
DateEvent
May 2019Published
13 March 2019Available
30 May 2018Accepted
Volume: 28
Number: 3
Page Range: pp. 465-472
DOI: 10.1017/S0963548318000421
Status: Peer Reviewed
Publication Status: Published
Reuse Statement (publisher, data, author rights): This article has been published in a revised form in Combinatorics, Probability and Computing https://doi.org/10.1017/S0963548318000421. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © copyright holder.
Access rights to Published version: Restricted or Subscription Access
Copyright Holders: © Cambridge University Press 2019
Date of first compliant deposit: 7 June 2018
Date of first compliant Open Access: 13 September 2019
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