A note on highly connected K_2,ℓ-minor free graphs

01/05/2023

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by   Nicolas Bousquet, et al.

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We show that every 3-connected K_2,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 K_2,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 K_2,ℓ-minor free graphs.