Reconfiguration Of Homomorphisms To Reflexive Digraph Cycles

Let G be a digraph and B be a fixed reflexive digraph cycle. Given two homomorphisms phi, phi' : G -> B, a walk from phi of phi' in the Hom-graph Hom(G, B) corresponds to what is often called a reconfiguration sequence of the homomorphisms. Except in the case that B contains a 4-cycle, containing an oriented cycle of algebraic girth 0, we give a polynomial time algorithm that either finds a path between two given homomorphisms or discovers an obstruction certifying the non-existence of such a path. (C) 2021 Elsevier B.V. All rights reserved.