Explicit bounds for graph minors

With this theorem, we derive explicit constants in the graph minor algorithms of Robertson and Seymour (1995) [10]. We reprove a result concerning redundant vertices for graphs on surfaces, but with explicit bounds. That is, we prove that there exists a computable integer t:=t(Σ,k) such that if v is a 't-protected' vertex in a surface Σ, then v is redundant with respect to any k-linkage.