A note on highly connected K_2,ℓ-minor free graphs
arxiv(2023)
摘要
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.
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