Determining triangulations and quadrangulations by boundary distances
We show that if all internal vertices of a disc triangulation have degree at least 6, then the full structure can be determined from the pairwise graph distances between boundary vertices. A similar result holds for disc quadrangulations with all internal vertices having degree at least 4. This conf...
| Main Author: | |
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| Format: | Journal article |
| Language: | English |
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Elsevier
2023
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| _version_ | 1797112707023896576 |
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| author | Haslegrave, J |
| author_facet | Haslegrave, J |
| author_sort | Haslegrave, J |
| collection | OXFORD |
| description | We show that if all internal vertices of a disc triangulation have degree at least 6, then the full structure can be determined from the pairwise graph distances between boundary vertices. A similar result holds for disc quadrangulations with all internal vertices having degree at least 4. This confirms a conjecture of Itai Benjamini. Both degree bounds are best possible, and correspond to local non-positive curvature. However, we show that a natural conjecture for a “mixed” version of the two results is not true. |
| first_indexed | 2024-03-07T08:27:40Z |
| format | Journal article |
| id | oxford-uuid:74c8067b-1b27-4112-8ece-ae4356a21a2e |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T08:27:40Z |
| publishDate | 2023 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:74c8067b-1b27-4112-8ece-ae4356a21a2e2024-02-27T09:46:55ZDetermining triangulations and quadrangulations by boundary distancesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:74c8067b-1b27-4112-8ece-ae4356a21a2eEnglishSymplectic ElementsElsevier2023Haslegrave, JWe show that if all internal vertices of a disc triangulation have degree at least 6, then the full structure can be determined from the pairwise graph distances between boundary vertices. A similar result holds for disc quadrangulations with all internal vertices having degree at least 4. This confirms a conjecture of Itai Benjamini. Both degree bounds are best possible, and correspond to local non-positive curvature. However, we show that a natural conjecture for a “mixed” version of the two results is not true. |
| spellingShingle | Haslegrave, J Determining triangulations and quadrangulations by boundary distances |
| title | Determining triangulations and quadrangulations by boundary distances |
| title_full | Determining triangulations and quadrangulations by boundary distances |
| title_fullStr | Determining triangulations and quadrangulations by boundary distances |
| title_full_unstemmed | Determining triangulations and quadrangulations by boundary distances |
| title_short | Determining triangulations and quadrangulations by boundary distances |
| title_sort | determining triangulations and quadrangulations by boundary distances |
| work_keys_str_mv | AT haslegravej determiningtriangulationsandquadrangulationsbyboundarydistances |