Domination, Packing and Excluded Minors

Let γ(G) be the domination number of a graph G, and let αk(G) be the maximum number of vertices in G, no two of which are at distance ≤ k in G. It is easy to see that γ(G) ≥ α2(G). In this note it is proved that γ(G) is bounded from above by a linear function in α2(G) if G has no large complete bipartite graph minors. Extensions to other parameters αk(G) are also derived.