Three algorithmic approaches to the general position problem
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911373126008832 |
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| author | Hamed-Labbafian, Zahra Sabeghi, Narjes Tavakoli, Mostafa Klavžar, Sandi |
| author_facet | Hamed-Labbafian, Zahra Sabeghi, Narjes Tavakoli, Mostafa Klavžar, Sandi |
| contents | If $G$ is a graph, then $X\subseteq V(G)$ is a general position set if for every two vertices $v,u\in X$ and every shortest $(u,v)$-path $P$, it holds that no inner vertex of $P$ lies in $X$. In this note we propose three algorithms to compute a largest general position set in $G$: an integer linear programming algorithm, a genetic algorithm, and a simulated annealing algorithm. These approaches are supported by examples from different areas of graph theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19389 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Three algorithmic approaches to the general position problem Hamed-Labbafian, Zahra Sabeghi, Narjes Tavakoli, Mostafa Klavžar, Sandi Combinatorics If $G$ is a graph, then $X\subseteq V(G)$ is a general position set if for every two vertices $v,u\in X$ and every shortest $(u,v)$-path $P$, it holds that no inner vertex of $P$ lies in $X$. In this note we propose three algorithms to compute a largest general position set in $G$: an integer linear programming algorithm, a genetic algorithm, and a simulated annealing algorithm. These approaches are supported by examples from different areas of graph theory. |
| title | Three algorithmic approaches to the general position problem |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2503.19389 |