Year: 2026
Type: preprint
Abstract: A family of paths in a graph $G$ strongly separates the edges of $G$ if for every ordered pair of distinct edges $(e,f)$ some path in the family contains $e$ and avoids $f$; the minimum size of such a family is denoted by $\operatorname{ssp}(G)$. Bonamy, Botler, Dross, Naia, and Skokan proved, for every $n$-vertex graph $G$, that $\operatorname{ssp}(G)\le 19n$; Liu, Xu, and Yang recently improved this to $\operatorname{ssp}(G)\le 10n-o(n)$. We prove, for every $n$-vertex graph $G$, that $\operatorname{ssp}(G)\le 7.75n$.
Source: arXiv (Cornell University)
Authors: Cranston, Daniel W., Noyman, Jared, Yu, Gexin
Institution: William & Mary
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7220907811