Homomorphisms of hexagonal graphs to odd cycles

The problem of deciding whether an arbitrary graph G has a homomorphism into a given graph H has been widely studied and has turned out to be very difficult. Hell and Nešetril proved that the decision problem is NP-complete unless H is bipartite. We consider a restricted problem where H is an odd cycle and G an arbitrary hexagonal graph. We show that any triangle-free hexagonal graph has a homomorphism into cycle C5.