On Separating Path and Tree Systems in Graphs
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913848249810944 |
|---|---|
| author | Biniaz, Ahmad Bose, Prosenjit De Carufel, Jean-Lou Maheshwari, Anil Miraftab, Babak Odak, Saeed Smid, Michiel Smorodinsky, Shakhar Yuditsky, Yelena |
| author_facet | Biniaz, Ahmad Bose, Prosenjit De Carufel, Jean-Lou Maheshwari, Anil Miraftab, Babak Odak, Saeed Smid, Michiel Smorodinsky, Shakhar Yuditsky, Yelena |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_14295 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On Separating Path and Tree Systems in Graphs Biniaz, Ahmad Bose, Prosenjit De Carufel, Jean-Lou Maheshwari, Anil Miraftab, Babak Odak, Saeed Smid, Michiel Smorodinsky, Shakhar Yuditsky, Yelena Discrete Mathematics Combinatorics 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. |
| title | On Separating Path and Tree Systems in Graphs |
| topic | Discrete Mathematics Combinatorics |
| url | https://arxiv.org/abs/2312.14295 |