A note on highly connected $K_{2,\ell}$-minor free graphs
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866929276764291072 |
|---|---|
| author | Bousquet, Nicolas Pierron, Théo Wesolek, Alexandra |
| author_facet | Bousquet, Nicolas Pierron, Théo Wesolek, Alexandra |
| contents | We show that every $3$-connected $K_{2,\ell}$-minor free graph with minimum degree at least $4$ has maximum degree at most $7\ell$. As a consequence, we show that every 3-connected $K_{2,\ell}$-minor free graph with minimum degree at least $5$ and no twins of degree $5$ has bounded size. Our proofs use Steiner trees and nested cuts; in particular, they do not rely on Ding's characterization of $K_{2,\ell}$-minor free graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_02133 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A note on highly connected $K_{2,\ell}$-minor free graphs Bousquet, Nicolas Pierron, Théo Wesolek, Alexandra Combinatorics Discrete Mathematics 05C75, 05C83 We show that every $3$-connected $K_{2,\ell}$-minor free graph with minimum degree at least $4$ has maximum degree at most $7\ell$. As a consequence, we show that every 3-connected $K_{2,\ell}$-minor free graph with minimum degree at least $5$ and no twins of degree $5$ has bounded size. Our proofs use Steiner trees and nested cuts; in particular, they do not rely on Ding's characterization of $K_{2,\ell}$-minor free graphs. |
| title | A note on highly connected $K_{2,\ell}$-minor free graphs |
| topic | Combinatorics Discrete Mathematics 05C75, 05C83 |
| url | https://arxiv.org/abs/2301.02133 |