A note on highly connected K2,ℓ-minor free graphs

We show that every 3-connected K2,ℓ-minor free graph with minimum degree at least 4 has maximum degree at most 7ℓ. As a consequence, we show that every 3-connected K2,ℓ-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 K2,ℓ-minor free graphs.