The maximum number of digons formed by pairwise crossing pseudocircles
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866912154675838976 |
|---|---|
| author | Ackerman, Eyal Damásdi, Gábor Keszegh, Balázs Pinchasi, Rom Raffay, Rebeka |
| author_facet | Ackerman, Eyal Damásdi, Gábor Keszegh, Balázs Pinchasi, Rom Raffay, Rebeka |
| contents | In 1972, Branko Grünbaum conjectured that any arrangement of $n>2$ pairwise crossing pseudocircles in the plane can have at most $2n-2$ digons (regions enclosed by exactly two pseudoarcs), with the bound being tight. While this conjecture has been confirmed for cylindrical arrangements of pseudocircles and more recently for geometric circles, we extend these results to any simple arrangement of pairwise intersecting pseudocircles. Using techniques from the above-mentioned special cases, we provide a complete proof of Grünbaum's conjecture that has stood open for over five decades. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_10023 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The maximum number of digons formed by pairwise crossing pseudocircles Ackerman, Eyal Damásdi, Gábor Keszegh, Balázs Pinchasi, Rom Raffay, Rebeka Combinatorics Computational Geometry In 1972, Branko Grünbaum conjectured that any arrangement of $n>2$ pairwise crossing pseudocircles in the plane can have at most $2n-2$ digons (regions enclosed by exactly two pseudoarcs), with the bound being tight. While this conjecture has been confirmed for cylindrical arrangements of pseudocircles and more recently for geometric circles, we extend these results to any simple arrangement of pairwise intersecting pseudocircles. Using techniques from the above-mentioned special cases, we provide a complete proof of Grünbaum's conjecture that has stood open for over five decades. |
| title | The maximum number of digons formed by pairwise crossing pseudocircles |
| topic | Combinatorics Computational Geometry |
| url | https://arxiv.org/abs/2412.10023 |