Span capacities of graphs
Fuente:
arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866916018323980288 |
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| author | Grašič, Mateja Mouron, Christopher Šubašić, Aljoša Taranenko, Andrej Vojković, Tanja |
| author_facet | Grašič, Mateja Mouron, Christopher Šubašić, Aljoša Taranenko, Andrej Vojković, Tanja |
| contents | The $d$-capacity of a graph $G$ is introduced as the maximum number of players that can simultaneously traverse $G$ such that each player visits all vertices while maintaining a distance of at least $d$ under various movement rules. We determine their values for paths and cycles and provide bounds for bipartite graphs. Furthermore, we characterize topfull graphs, where the 1-capacities reach their theoretical maximum, establishing a connection to graph factorizations and connectivity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_16852 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Span capacities of graphs Grašič, Mateja Mouron, Christopher Šubašić, Aljoša Taranenko, Andrej Vojković, Tanja Combinatorics The $d$-capacity of a graph $G$ is introduced as the maximum number of players that can simultaneously traverse $G$ such that each player visits all vertices while maintaining a distance of at least $d$ under various movement rules. We determine their values for paths and cycles and provide bounds for bipartite graphs. Furthermore, we characterize topfull graphs, where the 1-capacities reach their theoretical maximum, establishing a connection to graph factorizations and connectivity. |
| title | Span capacities of graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2605.16852 |