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On Separating Path and Tree Systems in Graphs
Published 21 Dec 2023 in cs.DM and math.CO | (2312.14295v3)
Abstract: We explore the concept of separating systems of vertex sets of graphs. A separating system of a set is a collection of subsets of such that for any pair of distinct elements in , 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 is called a vertex-separating path (tree) system of if the elements of the separating system are paths (trees) in the graph . 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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