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

doi:10.46298/dmtcs.12743

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

Department of Computer Science

Ben-Gurion University of the Negev

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Journal	DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE
Volume	272
DOIs	https://doi.org/10.46298/dmtcs.12743
State	Published - 1 Jan 2025

Keywords

separating set system
vertex-separating path system
vertex-separating tree system

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
General Computer Science
Discrete Mathematics and Combinatorics

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10.46298/dmtcs.12743

Cite this

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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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AU - Biniaz, Ahmad

AU - Bose, Prosenjit

AU - De Carufel, Jean Lou

AU - Maheshwari, Anil

AU - Miraftab, Babak

AU - Odak, Saeed

AU - Smid, Michiel

AU - Smorodinsky, Shakhar

AU - Yuditsky, Yelena

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AB - 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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On Separating Path and Tree Systems in Graphs

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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