Smooth Graphs
Fuente:
arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866911576396660736 |
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| author | Brešar, Boštjan Changat, Manoj Narasimha-Shenoi, Prasanth G. Schmidt, Bruno J. Stadler, Peter F. |
| author_facet | Brešar, Boštjan Changat, Manoj Narasimha-Shenoi, Prasanth G. Schmidt, Bruno J. Stadler, Peter F. |
| contents | The notion of smoothness was introduced originally in the context of step systems on connected graphs. Smoothness turns out to be a very general property of metrics defined by a five-point condition. Restricted to graphs, it is closely related to the convexity of point-shadows. We show that smoothness is preserved by isometric subgraphs, both Cartesian and strong graph products, and gated amalgams. As a consequence, median graphs and many of their generalizations are smooth. We also show that l1-graphs are smooth. On the other hand, an induced K2,3 or K1,1,3 is incompatible with smoothness. Finally, we characterize smooth graphs among the Ptolemaic graphs as precisely the K1,1,3-free Ptolemaic graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_07115 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Smooth Graphs Brešar, Boštjan Changat, Manoj Narasimha-Shenoi, Prasanth G. Schmidt, Bruno J. Stadler, Peter F. Combinatorics Metric Geometry 05C12 (Primary), 05C38, 05C76, 52A01 (Secondary) The notion of smoothness was introduced originally in the context of step systems on connected graphs. Smoothness turns out to be a very general property of metrics defined by a five-point condition. Restricted to graphs, it is closely related to the convexity of point-shadows. We show that smoothness is preserved by isometric subgraphs, both Cartesian and strong graph products, and gated amalgams. As a consequence, median graphs and many of their generalizations are smooth. We also show that l1-graphs are smooth. On the other hand, an induced K2,3 or K1,1,3 is incompatible with smoothness. Finally, we characterize smooth graphs among the Ptolemaic graphs as precisely the K1,1,3-free Ptolemaic graphs. |
| title | Smooth Graphs |
| topic | Combinatorics Metric Geometry 05C12 (Primary), 05C38, 05C76, 52A01 (Secondary) |
| url | https://arxiv.org/abs/2604.07115 |