  A graph K is square-free if it contains no four-cycle as a subgraph. A graph
K is multiplicative if GxH -> K implies G -> K or H -> K, for all graphs G,H.
Here GxH is the tensor (or categorical) graph product and G -> K denotes the
existence of a graph homomorphism from G to K. Hedetniemi's conjecture states
that all cliques K_n are multiplicative. However, the only non-trivial graphs
known to be multiplicative are K_3, odd cycles, and still more generally,
circular cliques $K_{p/q}$ with 2 <= p/q < 4. We make no progress for cliques,
but show that all square-free graphs are multiplicative. In particular, this
gives the first multiplicative graphs of chromatic number higher than 4.
Generalizing, in terms of the box complex, the topological insight behind
existing proofs for odd cycles, we also give a different proof for circular
cliques.
