Separating the edges of a graph by a linear number of paths

Bonamy, Marthe, Botler, Fábio, Dross, François, Naia, Tássio and Skokan, Jozef ORCID: 0000-0003-3996-7676 (2023) Separating the edges of a graph by a linear number of paths. Advances in Combinatorics. ISSN 2517-5599

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Abstract

Recently, Letzter proved that any graph of order n contains a collection P of O(nlog⋆n) paths with the following property: for all distinct edges e and f there exists a path in P which contains e but not f . We improve this upper bound to 19n, thus answering a question of G.O.H. Katona and confirming a conjecture independently posed by Balogh, Csaba, Martin, and Pluhár and by Falgas-Ravry, Kittipassorn, Korándi, Letzter, and Narayanan. Our proof is elementary and self-contained.

Item Type:	Article
Official URL:	https://www.advancesincombinatorics.com/
Additional Information:	© 2023 The Author(s)
Divisions:	Mathematics
Subjects:	Q Science > QA Mathematics
Date Deposited:	23 Oct 2023 11:06
Last Modified:	18 Nov 2024 20:03
URI:	http://eprints.lse.ac.uk/id/eprint/120514

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