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 .