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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2602.11657 |
| Etiquetas: |
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- We study the problem of finding, for a given one-dimensional topological space $X$, a cover of $X$ of smallest size by geodesics with respect to some metric. The infimal size of such a set is called the metric geodesic cover number of $X$. We prove reductions enabling us to find, with computer assistance, optimal geodesic covers of a graph and use these to determine the cover number of several standard graphs, including $K_4$, $K_5$ and $K_{3,3}$. We also give a catalogue of topological spaces with cover number $3$, and use it to deduce that any such space must be planar.