A note on highly connected $K_{2,\ell}$-minor free graphs
| Autor: | Bousquet, Nicolas, Pierron, Théo, Wesolek, Alexandra |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. |
| Databáze: | arXiv |
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