Recolouring homomorphisms to triangle-free reflexive graphs

For a graph H, the H-recolouring problem Recol (H) asks, for two given homomorphisms from a given graph G to H, if one can get between them by a sequence of homomorphisms of G to H in which consecutive homomorphisms differ on only one vertex. We show that, if G and H are reflexive and H is triangle-free, then this problem can be solved in polynomial time. This shows, at the same time, that the closely related H-reconfiguration problem Recon (H) of deciding whether two given homomorphisms from a given graph G to H are in the same component of the Hom-graph Hom (G, H) , can be solved in polynomial time for triangle-free reflexive graphs H.