Forest Cuts in Sparse Graphs
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_ | 1866912047187361792 |
|---|---|
| author | Chernyshev, Vsevolod Rauch, Johannes Rautenbach, Dieter |
| author_facet | Chernyshev, Vsevolod Rauch, Johannes Rautenbach, Dieter |
| contents | We propose the conjecture that every graph $G$ of order $n$ with less than $3n-6$ edges has a vertex cut that induces a forest. Maximal planar graphs do not have such vertex cuts and show that the density condition would be best possible. We verify the conjecture for planar graphs and show that every graph $G$ of order $n$ with less than $\frac{11}{5}n-\frac{18}{5}$ edges has a vertex cut that induces a forest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_17724 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Forest Cuts in Sparse Graphs Chernyshev, Vsevolod Rauch, Johannes Rautenbach, Dieter Combinatorics We propose the conjecture that every graph $G$ of order $n$ with less than $3n-6$ edges has a vertex cut that induces a forest. Maximal planar graphs do not have such vertex cuts and show that the density condition would be best possible. We verify the conjecture for planar graphs and show that every graph $G$ of order $n$ with less than $\frac{11}{5}n-\frac{18}{5}$ edges has a vertex cut that induces a forest. |
| title | Forest Cuts in Sparse Graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2409.17724 |