  We prove that for every path H, and every integer d, there is a polynomial f
such that every graph G with chromatic number greater than f(t) either contains
H as an induced subgraph, or contains as a subgraph the complete d-partite
graph with parts of cardinality t. For t = 1 and general d this is a classical
theorem of Gy\'arf\'as, and for d = 2 and general t this is a theorem of Bonamy
et al.
