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arXiv · 2312.14295

On Separating Path and Tree Systems in Graphs

Ahmad Biniaz·Prosenjit Bose·Jean-Lou De Carufel·Anil Maheshwari·Babak Miraftab·Saeed Odak·Michiel Smid·Shakhar Smorodinsky·Yelena Yuditsky
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Abstract

We explore the concept of separating systems of vertex sets of graphs. A separating system of a set $X$ is a collection of subsets of $X$ such that for any pair of distinct elements in $X$, there exists a set in the separating system that contains exactly one of the two elements. A separating system of the vertex set of a graph $G$ is called a vertex-separating path (tree) system of $G$ if the elements of the separating system are paths (trees) in the graph $G$. In this paper, we focus on the size of the smallest vertex-separating path (tree) system for different types of graphs, including trees, grids, and maximal outerplanar graphs.

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Ahmad Biniaz, Prosenjit Bose, Jean-Lou De Carufel, Anil Maheshwari, Babak Miraftab, Saeed Odak, Michiel Smid, Shakhar Smorodinsky, Yelena Yuditsky. 2023-12-21. On Separating Path and Tree Systems in Graphs. https://doi.org/10.46298/dmtcs.12743

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