  For a fixed graph H, the H-Recoloring problem asks whether for two given
homomorphisms from a graph G to H, we can transform one into the other by
changing the image of a single vertex of G in each step and maintaining a
homomorphism from G to H throughout. We extend an algorithm of Wrochna for
H-Recoloring where H is a square-free loopless undirected graph to the more
general setting of directed graphs. We obtain a polynomial-time algorithm for
H-Recoloring in this setting whenever H is a loopless digraph that does not
contain a 4-cycle of algebraic girth zero and whenever H is a reflexive digraph
that contains neither a 3-cycle of algebraic girth 1 nor a 4-cycle of algebraic
girth zero.
