Motivated by Hadwiger’s conjecture, Seymour asked which graphs H H have the property that every non-null graph G G with no H H minor has a vertex of degree at most | V (H) | − 2 |V (H) |-2. We show that for every monotone graph family F F with strongly sublinear separators, all sufficiently large bipartite graphs H ∈ F H F with bounded maximum degree have this property. None of the conditions that H H belongs to F F, that H H is bipartite and that H H has bounded maximum degree can be omitted.
Norin et al. (2025) studied this question.