Recently I cam across a statement which divides graphs into different classes w.r.t. the complexity of problems on them.
planar < bounded genus < H-minor free < general graphs
My question regards the definition of H-minor free graphs. What I don't understand is that apparently H is not fixed.
Is it true that as long as I can be sure that my (large) graph G doesn't contain some! minor, then some problems might be easier to compute on G then on general graphs regardless of what the actual minor is?