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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Text (Separating the Edges of a Graph by a Linear Number of Paths)
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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 |
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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: | 12 Aug 2024 03:13 |
URI: | http://eprints.lse.ac.uk/id/eprint/120514 |
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