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arXiv · 2301.08707

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

Marthe Bonamy·Fábio Botler·François Dross·Tássio Naia·Jozef Skokan
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Abstract

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

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Marthe Bonamy, Fábio Botler, François Dross, Tássio Naia, Jozef Skokan. 2023-01-20. Separating the edges of a graph by a linear number of paths. https://doi.org/10.19086/aic.2023.6

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