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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | https://arxiv.org/abs/2408.17234 |
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| _version_ | 1866909301450211328 |
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| author | Korže, Danilo Vesel, Aleksander |
| author_facet | Korže, Danilo Vesel, Aleksander |
| contents | For a given graph \(G\), the general position problem asks for the largest set of vertices \(M \subseteq V(G)\) such that no three distinct vertices of \(M\) belong to a common shortest path in \(G\). A relaxation of this concept is based on the condition that two vertices \(x, y \in V(G)\) are \(M\)-visible, meaning there exists a shortest \(x, y\)-path in \(G\) that does not pass through any vertex of \(M \setminus \{x, y\}\).
If every pair of vertices in \(M\) is \(M\)-visible, then \(M\) is called a mutual-visibility set of \(G\). The size of the largest mutual-visibility set of \(G\) is called the mutual-visibility number of \(G\). Some well-known variations of this concept consider the total, outer, and dual mutual-visibility sets of a graph.
We present results on the general position problem and the various mutual-visibility problems in Sierpiński triangle graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_17234 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mutual-visibility and general position sets in Sierpiński triangle graphs Korže, Danilo Vesel, Aleksander Combinatorics For a given graph \(G\), the general position problem asks for the largest set of vertices \(M \subseteq V(G)\) such that no three distinct vertices of \(M\) belong to a common shortest path in \(G\). A relaxation of this concept is based on the condition that two vertices \(x, y \in V(G)\) are \(M\)-visible, meaning there exists a shortest \(x, y\)-path in \(G\) that does not pass through any vertex of \(M \setminus \{x, y\}\). If every pair of vertices in \(M\) is \(M\)-visible, then \(M\) is called a mutual-visibility set of \(G\). The size of the largest mutual-visibility set of \(G\) is called the mutual-visibility number of \(G\). Some well-known variations of this concept consider the total, outer, and dual mutual-visibility sets of a graph. We present results on the general position problem and the various mutual-visibility problems in Sierpiński triangle graphs. |
| title | Mutual-visibility and general position sets in Sierpiński triangle graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2408.17234 |